Biography 

Nicolas Merlinge received the PhD degree from Coventry University and Université Paris-Saclay in 2018. He is currently a research scientist at ONERA - the French aerospace lab (Université Paris-Saclay). His research interests include nonlinear state estimation, system identification, and control for aerospace vehicles.

Set Inversion and Box Contraction on Lie groups Using Interval Analysis - Application to Bounded Attitude Estimation

Set inversion and box contraction consist in finding bounded solutions to an equation where variables belong to bounded sets. These problems are classic in Euclidean spaces and can be solved using interval analysis (e.g. with the SIVIA method and with interval contractors). However, they quickly become complex when dealing with non-Euclidean manifolds.
This presentation introduces a way to solve these problems when variables belong to generic Lie groups (e.g. the set of rotation matrices SO(3)). The core idea is to treat Lie group subsets via interval analysis in the vector space of the Lie algebra using the exponential mapping as a local bijection. Under this "Lie group interval" framework, SIVIA and generic contractors can be used, e.g. to solve bounded attitude estimation problems.

Biography 

Dr Jian Wan has been a lecturer in Mechatronics and Robotics in the School of Engineering and Technology, College of Engineering and Physical Sciences, Aston University since February 2022. Prior to that, Dr Wan had worked in the School of Engineering, Computing and Mathematics, the University of Plymouth as a lecturer in Control Systems Engineering from January 2015 to January 2022. He obtained his PhD in Control Engineering with summa cum laude in 2007 from the Department of Electronics, Computer Science and Automatic Control, University of Girona, Spain. His research interests include set-theoretic methods in control, machine learning, robotics and autonomous systems.

A Review of Set Representation, Partition and Propagation Techniques for Set-Theoretic Methods in Control

Set-theoretic methods refer to any method that exploits properties of sets or propagates various sets for dynamic systems through the integration of interval arithmetic, computational geometry, and other mathematical tools. So mathematical tools have always played a central role for the development of various set-theoretic methods. This talk reviews typical set representation, partition and propagation techniques for set-theoretic methods in control with the aim to break the boundaries as well as explore the synergies among these techniques for reducing wrapping effect and improving shape flexibility of set computation with successful applications to control.

Biography 

Nacim Meslem received a M.Sc. degree from Ecole Centrale de Nantes in 2004 and then a Ph.D. degree in engineering sciences from the University of Paris Est Créteil in 2008. Since 2012, he is an Associate Professor at the University of Grenoble Alpes, affiliated to  ENSE3 (National School of Energy, Water and Environment) Grenoble, France. He is a member of Gipsa-lab (Grenoble Images Speech Signal and Control laboratory). His research interests include set-membership estimation, event-based control and estimation, and airborne wind-energy systems.

Secure State Estimation Algorithm for Discrete-Time Linear Systems: A Set-Valued Approach

Based on consistency techniques, a set-valued algorithm is proposed to estimate the actual state vector of discrete-time linear systems in the presence of both bounded uncertainties and sensor anomalies. This algorithm can be considered as an extension of a former predictor-corrector set-valued state estimator to the case where the feasible domains of the bounded uncertainties are time-varying. Moreover, the introduced algorithm comprises several set-membership tests that allow detecting the occurrence of sensor faults or output malicious attacks and then discarding them from the estimation process. Moreover, to defeat the attacker’s strategy only a sub-set of the available sensors is selected randomly, at each time instant, to improve the efficiency of the estimation algorithm.

Biography 

Amr Alanwar has been an assistant professor at the Technical University of Munich since September 2023. He was a professor at Constructor University at Bremen before that. Amr was a postdoctoral researcher at the KTH Royal Institute of Technology. He got his Ph.D. with the Cyber-Physical Systems Group at the Technical University of Munich (TUM) in 2020. Before that, he was a research assistant at the University of California, Los Angeles (UCLA). Amr won the Best Demonstration Paper Award at the 16th ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN/CPS week) and was a finalist in the Qualcomm Innovation Fellowship for two years in a row. He received his B.Sc. and M.Sc. from Ain Shams University in Egypt. His current research interests include safety, privacy, and general topics in cyber-physical systems.

Reachability Analysis for Logical Systems Using Logical Zonotopes and their Polynomial Extension

Logical systems have been used to model complex behaviors in numerous applications. An important form of analysis for logical systems is reachability analysis, which allows us to formally verify the behavior of logical systems and provide guarantees that, for example, the system will not enter into undesired states. This talk introduces an approach to enhance the efficiency of reachability analysis in logical systems through the utilization of binary set representations known as logical zonotopes and their extension, polynomial logical zonotopes. A logical zonotope can efficiently represent up to 2^n binary vectors using only n generators. Due to their construction, logical zonotopes are only able to support exact computations of some logical operations (XOR, NOT, XNOR), while other operations (AND, NAND, OR, NOR) result in over-approximations. In order to perform all fundamental logical operations exactly, a generalization of logical zonotopes is formulated in a polynomial-like construction in which all of the fundamental logical operations (XOR, NOT, XNOR, AND, NAND, OR, NOR) can be performed exactly.

Biography 

Thomas Lew is a Research Scientist at the Toyota Research Institute. He completed his PhD degree in Aeronautics and Astronautics at Stanford University in 2023, his MSc degree at ETH Zürich in 2019, his BSc degree at EPFL in 2017, and research internships at Google Brain Robotics and at the NASA Jet Propulsion Laboratory. His research focuses on the design of decision-making algorithms for autonomous systems. He is a recipient of the 2023 IEEE Conference on Decision and Control Outstanding Student Paper Award and of the 2023 IEEE Control Systems Magazine Outstanding Paper Award.

Exact Characterization of the Convex Hulls of Reachable Sets

In this talk, I will present a new characterization of the convex hulls of reachable sets of a class of nonlinear systems with disturbances. Reachable sets play an important role in control, but remain challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. Our result states that the convex hulls of reachable sets are exactly the convex hulls of solutions of an ordinary differential equation from all possible initial values of the disturbances. This finite-dimensional characterization unlocks a fast sampling-based method to accurately over-approximate reachable sets. I will present applications to neural feedback loop analysis and robust model predictive control.

Biography 

Antoine Hugo obtained the Engineering degree in 2020 from the École nationale supérieure d'électrotechnique, d'électronique, d'informatique, d'hydraulique et des télécommunications (ENSEEIHT) of Toulouse, France. Since November 2021, he has been a PhD student at the Institut de Recherche en Systèmes Electroniques Embarqués (IRSEEM) and the Office National d'Etudes et de Recherches Aérospatiales (ONERA). His research interests include state estimation and control of uncertain systems using set-membership techniques, with application to autonomous vehicles.

Filtered High Gain Interval Observer for LPV System with Bounded Uncertainties

State estimation of uncertain systems is a challenging task. Uncertainties are often due to insufficient knowledge about the system itself or its environment. Among the deterministic approaches to tackle this issue, High Gain Observers and Interval Observers are two popular methodologies. However, the combination of both has only been a little explored in the literature. It is in this perspective that this talk will present a new High-Gain Interval Observer (HGIO) for a class of Linear Parameter Varying (LPV) systems subject to bounded additive disturbances and measurement noise. Then, in order to mitigate the measurement noise amplification, an output error filter is incorporated in the design which leads to the Filtered High-Gain Interval Observer (FHGIO). Some suitable changes of coordinates are used to ensure the cooperativity of the error dynamics which is one of the key concepts of interval observer design. Moreover, the gains design and the stability analysis will be covered. For the latter, a sufficient non-divergence condition must be verified. Those observers have the advantage that their convergence speed and estimated interval width can be tuned by a unique parameter, the high-gain parameter.

Biography 

Michel Kieffer is a Full Professor in Signal Processing for Communications with the Université Paris-Saclay and a researcher with the Laboratoire des Signaux et Systèmes, Gif-sur-Yvette, France. From 2009 to 2015, he was a part-time Invited Professor with the Laboratoire Traitement et Communication de l’Information, Télécom ParisTech, Paris, France. He is coauthor of more than 200 contributions in journals, conference proceedings, or books. He is one of the coauthors of the books Applied Interval Analysis (Springer-Verlag, 2001) and Joint Source-Channel Decoding: A Cross-Layer Perspective with Applications in Video Broadcasting (Academic, 2009).
His research interests are in signal processing for multimedia, communications, and networking; distributed source coding; network coding; joint source-channel coding and decoding techniques. Applications are mainly in the reliable delivery of multimedia contents over wireless channels. He is also interested in guaranteed and robust parameter and state bounding for distributed systems in a bounded-error context.
Prof. Kieffer was a junior member of the Institut Universitaire de France from 2011 to 2016. He serves as an Associate Editor of Signal Processing since 2008 and of has been Associate Editor of the IEEE Transactions on Communications from 2012 to 2016.

Guaranteed Characterization of Exact Non-Asymptotic Confidence Regions Using Interval Analysis

In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. Usually, the estimation uncertainty is assumed to be Gaussian with the inverse of the Fisher information matrix evaluated at the estimate as covariance matrix. Nevertheless, this approach is only valid asymptotically (when the number of measurements tends to infinity) and provides an approximate characterization of the estimation uncertainty.
This talk overviews several approaches for exact and non-asymptotic confidence region characterization. They mainly differ by the assumptions considered on the measurement noise affecting the data used for the estimation. It will be shown that all of them lead to set-inversion problems, which may be efficiently solved using various tools from interval analysis. Asymptotic and non-asymptotic confidence region characterization will be compared on a distributed source localization problem.

Biography 

Lorenz Gillner received his B.Sc. degree in Applied Computer Science and Multimedia Engineering in 2020 as well as his M.Sc. degree in Applied Computer Science in 2022, both from the University of Applied Sciences Wismar, Germany. Since 2022 he has been a Research Assistant with the University of Applied Sciences Wismar, where is is working towards his PhD degree in collaboration with the Carl von Ossietzky Universität Oldenburg, Germany.

Interval Methods for the GPU in Global Optimization

Graphics processing units (GPUs) have long outgrown their original use as dedicated co-processors for computer graphics, due to their generational gain in performance. Modern GPUs are used as accelerators in various domains, such as cryptography, engineering or molecular research. Especially in the context of scientific computing, increasingly more software is targeting specialized hardware for data intensive workloads. Most interval libraries, on the other hand, were designed for sequential computations, while their CPU-specific implementations limit portability. In this talk, we present the current state of the art concerning interval software for GPUs and investigate the parallelization of interval methods in a global optimization scenario.

Biography 

Quentin Brateau received a double degree in Mobile Robotics, from ENSTA Bretagne, and in Dynamical Systems and Signals, from Polytech Angers, in 2021. He is currently a Ph.D. student at ENSTA Bretagne, in the Lab-STICC laboratory, on the control of torpedo-like AUVs. His research is focused on the control and state estimation of such robots in constrained environments.

Union of Adjacent Contractors

The union of contractors is a fundamental operation in contractor programming. It is used to build more complex contractors from fundamental ones. However, the union of adjacent contractors can reveal the common boundary between the two contractors, which is not consistent with the set union as defined in set theory. This problem is particularly noticeable in geometric contractors, which are a class of contractors based on geometric constraints, and in which contractors are often adjacent. This presentation will focus on the problem statement, and provide some insight to build contractors on the union instead of relying on the union of contractors.

Biography 

Dr. Daniel Silvestre received his B.Sc. in Computer Networks in 2008 from the Instituto Superior Técnico (IST), Lisbon, Portugal, and an M.Sc. in Advanced Computing in 2009 from the Imperial College London, London, United Kingdom. In 2017, Dr. Silvestre got his Ph.D. (with the highest honors) in Electrical and Computer Engineering from the former university, and during this period he spent three months visiting his co-supervisor (Joao Hespanha) at University of California at Santa Barbara. Currently, Dr. Silvestre is an Assistant Professor at Faculty of Science and Technology from the NOVA University of Lisbon (PT). His research interests span the fields of set-valued estimation, fault detection and isolation, distributed systems, network control systems, nonlinear optimization and model predictive control.

Constrained Convex Generators: A Set Representation for Accurate Estimation

In order to produce set-valued estimation for a dynamical system, one needs to be able to incorporate different types of bounds for the unknown signals and deal with uncertainty in the dynamics. However, in order to produce accurate estimation there is typically a trade-off with computation time since the growth of the data structures for the sets rapidly increases. In this talk, we will first go over the applications where set membership techniques are a relevant approach and then start with Linear Systems with no uncertainties. We will explore what can be obtained for the various classes of systems when using Constrained Convex Generators (CCGs) before showing how to deal with uncertainties in the model. Besides highlighting implementation issues like order reduction methods and techniques to avoid the growth of the data structures, we will also cover some recent work in extending CCGs to nonlinear systems.

Biography 

Dr. Sze Zheng Yong is an Associate Professor in the Mechanical and Industrial Engineering Department at Northeastern University. Prior to that, he was an Assistant Professor with the School for Engineering of Matter, Transport and Energy, Arizona State University and a postdoctoral fellow in the Department of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. He received a Dipl.-Ing. (FH) degree in Automotive Engineering with a specialization in mechatronics and control systems from the Esslingen University of Applied Sciences, Germany in 2008, and S.M. and Ph.D. degrees in Mechanical Engineering from Massachusetts Institute of Technology, Cambridge, MA in 2010 and 2016, respectively. He was the recipient of the DARPA Young Faculty Award in 2018, the NSF CAREER and NASA Early Career Faculty awards in 2020, the ONR Young Investigator Program Award in 2022, and the George N. Saridis Best Transactions Paper Award in 2023. His research interests include the broad areas of control, estimation, planning, learning and analysis of hybrid systems, with applications to autonomous, robotic and cyber-physical dynamic systems.

Robust Control Barrier Functions with Set-Membership Estimation and Learning

Recent research in safety control has leveraged the availability of accurate models to detect impending safety violations and to intervene accordingly. However, there is often a mismatch between the models that are used for algorithm design and the real systems. Thus, this talk introduces robust control barrier functions for two classes of uncertain systems. For the first class of uncertain parametric control affine systems, methods based on mixed-monotone decomposition and robust optimization are presented, where the robust controlled invariance condition remains linear in the control inputs despite nonlinear and time-varying uncertainties. In addition, our design includes set-membership estimation based on interval observers to reduce the conservatism of the proposed robust control barrier functions. Next, a novel robust data-driven control barrier function is introduced for the class of uncertain continuous systems to guarantee robust safety despite worst-case realizations of generalization errors from prior data. In particular, under various continuity assumptions, we leverage set-membership learning approaches for learning guaranteed upper and lower bounds of an unknown function from the data set to obtain a safe input set for robust controlled invariance. Finally, the talk will conclude with a brief discussion of some future opportunities and challenges for guaranteeing safety of uncertain systems.

Biography 

Currently, I am a Postdoctoral Scholar at the Department of Mechanical and Aerospace Engineering at the University of California, San Diego (UCSD), working with Prof. Sonia Martínez. I received my Ph.D. in Mechanical Engineering from Arizona State University (ASU) in 2021, where I worked in the Intelligent Control and Estimation of Things (ICE-T) Laboratory under the tutelage of Prof. Sze Zheng Yong. My Ph.D. thesis received the 2021 ASU Dean’s Dissertation Award in the Ira A. Fulton Schools of Engineering. I author or co-author diverse papers published in refereed conference proceedings and journals. My research interests lie broadly in designing tractable and computationally efficient set-theoretic methods for resilient, robust, and private estimation, learning, optimization, and control of complex safety-critical networked cyber-physical systems.

Remainder-Form Decomposition Functions & Their Applications to Guaranteed Reachability, Interval Observer Design & Resilient Estimation

Concerning designing robust, safe, and secure estimation and control algorithms, in this talk, I will first introduce the notion of "mixed-monotone remainder-form decomposition functions" and discuss how they contribute to the reachability of constrained nonlinear systems [1]. Then, I will show how the idea of mixed-monotone decomposition/inclusions can be applied to robust reachability analysis, interval observer design, and secure input and state estimation of nonlinear continuous-time and discrete-time systems [2,3,4].

Finally, I will discuss some future visions on mixed-monotonicity  that I'm interested to pursue. 

References:

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10057091

[2] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9790824

[3] https://par.nsf.gov/servlets/purl/10323416

[4] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9867885

Biography 

Morgan Louedec received a general engineering degree at the Ecole Centrale Nantes and a master of science in Electrical Engineering at the Technical University of Denmark in 2021. Since 2021, he is preparing for his Ph.D. at the LAB-STICC within ENSTA Bretagne, Brest, France, on the topic of stability of groups of robots. His research interests are stability analysis of dynamical systems and guaranteed numerical tools.

Encompassing Computation of the Ellipsoidal Image in the Singular Case

Several set analysis methods for dynamical systems consider the propagation of ellipsoids through nonlinear mappings. Recent works have proposed an algorithm evaluating the image of an ellipsoid by non-linear mappings, using an ellipsoid encompassing the image of the first. This method assumes that the Jacobian matrix of the mapping is square and invertible at the point of linearization. However, there are various systems where this assumption does not hold. This presentation proposes an extension of the method in the singular case.

Biography 

Martin Fränzle has been the Professor (W2) for “Hybrid Systems” and "Foundations and Applications of Systems of Cyber-Physical Systems" (W3) within the Department of Computing Science at the University of Oldenburg since 2004 and 2022, resp. Holding a diploma and a doctoral degree in Computer Science from the University of Kiel, he spent two years researching and teaching as an Associate Professor in Computer Science and Engineering at the Technical University of Denmark (DTU) located at Kongens Lyngby in the Copenhagen area, where he subsequently also held a Velux Visiting Professorship for the years 2006 to 2008. He was the Dean of the School of Computing Science, Business Administration, Economics, and Law at Oldenburg University, was long-standing member of the university’s Academic Senate and its commissions, and was the Vice President for Research, Transfer, and Digitalization at the University of Oldenburg for the years 2020 and 2021. 

His research spans a scope from fundamental research, in particular dynamic semantics and decidability issues of formal models of cyber-physical systems, over technology development addressing tools for the modelling, automated verification, and synthesis of cyber-physical and human-cyber-physical system designs to applied research as well as technology transfer with automotive industries and tool vendors.

Towards Truly Robust Spatio-Temporal Monitoring: Monitoring Safety Properties of Interacting Cyber-Physical Systems under Uncertain Observation

A signal-based interpretation of linear-time temporal logic permits classifying the time-dependent signals originating from continuous-state or hybrid-state dynamical systems according to formal specifications. Especially Signal Temporal Logic has been conceived as a tool for systematizing the monitoring of cyber-physical systems, supporting the automatic translation of complex safety specifications into efficient monitoring algorithms faithfully representing their semantics. Most algorithms hitherto suggested do, however, assume perfect identity between the sensor readings informing the monitor about the system state and the actual ground truth. Only recently have Visconti et al. addressed the issue of inexact measurements, taking up the simple model of interval-bounded per-sample error. In their model, the error is unrelated, in the sense of chosen afresh, across samples. In the talk, which reports on joint work with Bernd Finkbeiner, Florian Kohn, and Paul Kröger, we expand their analysis by decomposing the error into an unknown yet fixed offset and an independent per-sample error and show that in this setting, monitoring of temporal properties no longer coincides with collecting Boolean combinations of state predicates evaluated in each time instant over best-possible per-sample state estimates, but can be genuinely more informative in that it infers determinate truth values for monitoring conditions that interval-based evaluation remains inconclusive about. For the model-free as well as for the linear model-based case, we provide optimal evaluation algorithms based on affine arithmetic and SAT modulo theory solving over linear arithmetic. The resulting algorithms provide conclusive monitoring verdicts in many cases where state estimations inherently remain inconclusive. In their model-based variants, they can simultaneously address the issues of uncertain sensing and partial observation.



In a second part of the talk, I will report on algorithms developed with Kim G. Larsen, Thomas M. Grosen, and Martin Zimmermann that transfer such optimal monitoring under uncertainty from state uncertainty to timing uncertainty. In the corresponding model, the time stamps of observations are uncertain by an unknown (yet generally bounded) time offset due to delay in the communication channel. This offset can then be decomposed into a base delay that stays fixed across samples and a jitter that varies from sample to sample. Such an error model pertains to networked control systems, where properties are observed through a network featuring delay and jitter in message forwarding.

Biography 

Hao Liu received the B.Sc. degree in aircraft engineering in 2007 from Shenyang  Institute of Aeronautical Engineering, M.Sc. degree in aircraft design in 2009 from Harbin Institute of Technology, and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, respectively. Between February 2012 and August 2012, he was a visiting scholar in IMT Institute for Advanced Studies Lucca, Italy. He is currently an associate professor in the Shenyang Aerospace University.  His current research interests include cyber attacks, switched systems, multi-agent system, and reinforcement learning.

Watermark-based Proactive Defense Strategy Design For Cyber-Physical Systems With Unknown-but-bounded Noises

A proactive attack defense strategy dealing with the secure remote estimation issue in cyber-physical systems (CPS) with unknown-but-bounded (UBB) noises in the presence of man-in-the-middle (MITM) attacks is presented during this seminar. It is assumed that the residue calculated by the smart sensor is sent to the remote estimator and the abnormal intrusion detector via a wireless network, and the watermark is assumed to belong to a zonotope. In order to guarantee the detection rate, the data processes and the watermark are time-varying and secret to an adversary. Moreover, the effect on system performance caused by the watermark can be removed when the system is attack-free. Furthermore, four different attack scenarios are discussed to analyze the detection ability of the proposed defense approach, and the designed strategy can be applied to detect replay attacks. Finally, an unmanned aircraft system (UAS) subject to malicious attacks is leveraged to illustrate the effectiveness of the proposed proactive defense strategy.

Biography 

Feng XU is an Assistant Professor with Tsinghua Shenzhen International Graduate School, Tsinghua University, China. He received his Bachelor's degree in Measurement and Control Technology and Instrumentation from Northwestern Polytechnical University, Xi'an, China, in July 2010. In December 2014, he obtained his Ph.D. degree with honor in Automática, Robótica y Visión from Universitat Politècnica de Catalunya - BarcelonaTech, Barcelona, Spain. During the Ph.D. period, he was also a jointly-training Ph.D. student at CentraleSupélec, Paris, France. From June 2015 to July 2017, he was a Postdoctoral Fellow in Control Science and Engineering, Tsinghua University. He is an IEEE Senior Member and works on fault diagnosis, state estimation and fault-tolerant control.

Set Separation and Exclusion Tendency-Based Design Framework for Active Fault Diagnosis

Active fault diagnosis (AFD) designs inputs to excite the system to obtain more fault information for diagnosis and thus has ability to diagnose more faults than passive fault diagnosis. Under the set-theoretic framework, the classical methods are to design an N-step input sequence to separate all output estimation sets of different healthy and faulty system modes at a time such that diagnosis is finally achieved. However, this idea results in high computational complexity due to solving complex optimization problems. In order to overcome the computational complexity problem, the speaker and his collaborators have recently developed a new AFD method using set-valued observers. The key idea behind this new method includes two steps. The first step is to design inputs and observer gains step by step to increase the separation tendency of output estimation sets instead of designing an N-step input sequence to separate them at a time. The second step is to optimize observer gains to maximize the exclusion tendency of the output from output estimation sets such that the diagnosis performance is further improved. The two steps together form a set separation and exclusion tendency-based logic to implement AFD. At the end of this talk, examples are used to illustrate the effectiveness of this newly-developed method.

References:

1. F. Xu. Observer-Based Asymptotic Active Fault Diagnosis: A Two-Layer Optimization Framework. Automatica, 128:109558, 2021.
2. Y.D. Fan, F. Xu, X.Q. Wang and B. Liang. Exclusion Tendency-Based Observer Design Framework for Active Fault Diagnosis. Automatica, In press, 2023.

Biography 

Sabine Lerch graduated in the field of Electrical Engineering at the University of Wuppertal (Germany) in 2017. Since 2018, she is a PhD student at the Chair of Automation Engineering and Control Systems at the University of Wuppertal. Her main research field is the development of generic LMI algorithms for the design and optimization of controllers for discrete-time multivariable systems with actuator magnitude and rate saturation.

Minimizing Oscillations for Magnitude and Rate Saturated Discrete Time Systems by a DR Region Pole Placement

Often a controller is designed to act particularly fast in order to reach an operating point in the shortest possible time. However, this can lead to oscillations in the input and output variables. Also, real actuators are delimited in their magnitude and rate, which can lead to instability, if those boundaries are not considered in the controller design. This talk addresses a controller design method for discrete-time linear systems subject to magnitude and rate-saturated actuators. Thereby, oscillations are minimized by a pole placement within a convex approximation of the cardioid contour of constant damping. Stability is ensured by a quadratic Lyapunov function, whereby the nonlinear twofold actuator saturation is included in a convex hull. To design different controller types, an iterative LMI method is presented. The results are exemplary demonstrated by simulations of numerical examples as well as real applications for different controller types.

Reference:

S. Lerch, R. Dehnert, M. Rosik and B. Tibken, "Minimizing Oscillations for Magnitude and Rate-Saturated Discrete-Time Systems by a DR Region Pole Placement," 2022 10th International Conference on Systems and Control (ICSC), Marseille, France, 2022, pp. 244-249, doi: 10.1109/ICSC57768.2022.9993891

Eigenvalues, Eigenvectors and a Spectral Decomposition of an Interval Matrix

The matrix spectral properties play an important role in control theory, e.g., in stability analysis. If we model uncertainty, which is quite common in real life, by means of interval analysis, we immediately encounter spectral problems of interval matrices. This presentation aims to provide the participants with an overview of basic enclosures and computational properties of eigenvalues and eigenvectors of interval matrices. We also present some recent results on computation of a spectral decomposition of interval matrices, both for general interval matrices as well as its modification for symmetric interval matrices. Eventually, we show an application of the spectral decomposition to computing powers of interval matrices.

References:

1. D. Hartman, M. Hladík, and D. Říha. Computing the spectral decomposition of interval matrices and a study on interval matrix powers. Appl. Math. Comput., 403:126174:1-13, 2021.
2. J. Rohn. A handbook of results on interval linear problems. Technical Report 1163, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, 2012. http://hdl.handle.net/11104/0212095

Preliminary Design of an Interval-Based Autopilot

An autopilot is a combination of an INS (Inertial Navigation System), additional predefined sensors, actuators, and communication ports, with control algorithms. Its purpose is to provide the best state estimation of a robot in all conditions as well as autonomous operation such as following waypoints. Some experiments show that recurring causes of mission failures and robot loss are related to a wrong heading and/or position estimation, often due to a problem on one sensor even though other related sensors were correct.This presentation proposes to demonstrate how an interval-based heading estimation algorithm could help detecting and correcting some sensors inconsistencies by design. The results of experiments with an autonomous boat will show the practical use of the method, see [1].

Reference

[1] F. Le Bars, R. Sanchez, L. Jaulin, S. Rohou, and A. Rauh, An online interval-based inertial navigation system for control purposes of autonomous boats, Frontiers Control Engineering, Special issue: Reliable Modeling, Simulation, Identification, Control and State Estimation for Dynamic Systems with Uncertainty, 2021. (https://10.3389/fcteg.2021.786188)

Interval Impulsive Observers: A Framework for Robust Estimation with Aperiodic or Event-Triggered Sampling

The talk addresses interval state estimation in networked control systems. There has been a significant development of embedded and networked control systems, where sensor and control data are transmitted over digital communication channels. To reduce the communication load on these limited bandwidth channels, it is tempting to exchange data in an aperiodic manner. Besides, the presence of sampling jitters, packet dropouts and fluctuations in network accessibility further emphasized the interest in time-varying and aperiodic sampling. 

The talk objectives are twofold: 1) introduces the concept of interval impulsive observer, a new framework for interval state estimation for continuous dynamical systems from discrete-time measurements, 2) show how to use interval impulsive observers for designing robust interval with either aperiodic or event-triggered sampling. 

This is a work jointly conducted with Dr. Djahid Rabehi (PRISME - Univ. Orleans) and Dr. Nacim Meslem (GIPSA Lab).

References

1. Djahid Rabehi, Nacim Meslem, Adnen Amraoui, Nacim Ramdani. Interval impulsive observer for linear systems with aperiodic discrete measurements. IEEE Transactions on Automatic Control 66(11), pp. 5407-5413, 2021 doi:10.1109/TAC.2020.3046126 
2. Djahid Rabehi, Nacim Meslem, Nacim Ramdani. Finite-gain L1 Event-triggered Interval Observers design for Continuous-time Linear Systems. Int. Journal of Robust and Nonlinear Control 31, 4131-4153, 2021, doi:10.1002/rnc.5463.
   
   

Convexification Techniques for Stationary/Dynamic Global Optimization and Set-Based Computing

In this talk, we review some state-of-the art approaches to convexification of algebraic (factorable) functions and to the bounding of the solutions of parametric ordinary differential equations. Particularly, we present interval and Taylor model formalisms. The applications include stationary as well as dynamic optimization, functional analysis under uncertainty, and set-based computation tools. We discuss in detail the use of the presented tools in set-membership estimation.

References

1. N. Peric, R. Paulen, M. Villanueva, B. Chachuat: Set-membership nonlinear regression approach to parameter estimation. Journal of Process Control, vol. 70, pp. 80–95, 2018.
2. R. Paulen, M. Villanueva, B. Chachuat: Guaranteed parameter estimation of non-linear dynamic systems using high-order bounding techniques with domain and CPU-time reduction strategies. IMA Journal of Mathematical Control and Information, no. 3, vol. 33, pp. 563–587, 2016.
3. B. Chachuat, B. Houska, R. Paulen, N. Peric, J. Rajyaguru, M. Villanueva: Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems. In 9th International Symposium on Advanced Control of Chemical Processes ADCHEM 2015 Whistler, British Colombia, Canada, 7-10 June 2015, pp. 982–996, 2015.
   

Distribution-Free Bayesian Updating with Hybrid Uncertainties

The complexity of model updating depends on the presence of different level of aleatory and epistemic uncertainties. Deterministic model updating generally accounts for the presence of only epistemic uncertainty, where parameters are fixed but unknown constants.

On the other hand, the presence of hybrid uncertainties is considered by Bayesian model updating, where the aim is not only a single set of parameters, but a reduced space of epistemic variables which can represent model predictions in agreement to a multiple sets of observations.

In the presence of hybrid uncertainties, parameters are modeled as random variables with only vaguely determined uncertainty characteristics, e.g., by means of p-boxes. However, analysts need to assume a distribution family for the epistemic parameter. This is a very significant assumption that greatly constrains the possibility to accurately capture the real variation affecting the physical system. Thus, staircase random variables are employed in this presentation to characterize epistemic uncertainties without any pre-hypotheses of the distributional characteristics. Additionally, a two-step approximate Bayesian computation is employed, where the Euclidian and Bhattacharyya distances are utilized as uncertainty quantification metric.

The performance of the proposed procedure is demonstrated with an illustrative application using a shear building model and the 2020 NASA challenge.

References

1. M. Kitahara, S. Bi, M. Broggi, M. Beer: Nonparametric Bayesian stochastic model updating with hybrid uncertainties; Mechanical Systems and Signal Processing 163, 2022, 108195
2. A. Lye, M. Kitahara, M. Broggi, E. Patelli: Robust optimization of a dynamic Black-box system under severe uncertainty: A distribution-free framework; Mechanical Systems and Signal Processing 167, 2022, 108522
3. S. Bi, M. Broggi, M. Beer: The role of the Bhattacharyya distance in stochastic model updating; Mechanical Systems and Signal Processing 117, 2019, 437-452
   

Intervals in Fault-Free Error Modeling for GNSS Applications

Nowadays, the Global Navigation Satellite System (GNSS) is widely applied for transportation navigation. These applications can be safety-critical, such as autonomous driving, where high-integrity performance of the navigation system must be ensured. Therefore, approaches to integrity monitoring (i.e., the assessment of trust that we can put into a navigation solution) have been investigated to protect users against potential integrity threats. Crucial questions include: how representative the point positions are and how their uncertainty can be safely bounded. In this regard, the effective uncertainty budget is of vital importance. This does not only mean the random variability of the observations (stochasticity), but also remaining systematic errors as a second – sometimes dominant – component.

Intervals can be seen as a natural way to bound observation uncertainty in navigation systems, since they are in principle free of any assumption about probability distributions and can thus describe adequately remaining systematic effects. Transferring the uncertainty from the observation domain to the state domain, such as the position and pose, the uncertainty is represented as a set-value, e.g., polytope, zonotope and interval box. This is applicable in navigation integrity monitoring as an alternative approach for error bounding, in contrast to conventional stochastic handling. The critical issue is how to determine the observation uncertainty interval properly.

In this talk, we report methods we have applied in the context of GNSS range-based positioning and show examples of uncertainty intervals due to different error sources in GNSS signal propagation. After that, we discuss how the subsequent set representation can be used in fault-free error modeling for GNSS integrity monitoring.

References

Su, J., & Schön, S. (2022). Deterministic approaches for bounding GNSS uncertainty: A comparative analysis. In 2022 10th Workshop on Satellite Navigation Technology (NAVITEC) (pp. 1-8). IEEE. DOI: 10.1109/NAVITEC53682.2022.9847545

Su, J., & Schön, S. (2022). Advances in Deterministic Approaches for Bounding Uncertainty and Integrity Monitoring of Autonomous Navigation. In Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022) (pp. 1442-1454). DOI: 10.33012/2022.18418

Exponential Stability Analysis of Linear (Irrational) Systems in the Parametric Space - A Constraint Satisfaction Problem

joint work of: Rachid Malti (1), Milan R. Rapaić (2), Vukan Turkulov (2): (1) Université de Bordeaux, France, (2) University of Novi Sad, Serbia.

This talk presents some new results, concerning robust stability analysis of LTI systems having irrational transfer functions which cover a wide variety of linear systems including distributed parameter systems that are solutions of partial differential equations, time-delay rational systems, and fractional order systems. Systems described by irrational transfer functions may be of infinite dimension, typically having an infinite number of poles and/or zeros, rendering their stability analysis more challenging as compared to their finite-dimensional counterparts. First, it is proven that, under mild hypotheses, new poles may appear to the right of a vertical axis of abscissa γ (when γ = 0: imaginary axis) through a continuous variation of parameters only if existing poles to the left of γ cross the vertical axis. Hence, by determining parametric values for which the crossing occurs, known as stability crossing sets (SCS), the entire parametric space is separated into regions within which the number of right-half poles (including multiplicities) is invariant. Based on the aforementioned result, a robust estimation algorithm of the SCS is formulated as an interval constraint satisfaction problem and solved using guaranteed methods from interval arithmetics. The developed algorithm is applied for assessing stability of (i) a controlled parabolic 1D partial differential equation, namely the heat equation, in finite and semi-infinite media, (ii) time-delay rational systems with distributed and retarded type delays, (iii) fractional systems, providing stability results even for incommensurate differentiation orders. This work is currently under review for a possible publication in an IFAC journal (Malti et al. 2023).

Reference

Malti, R., M. R. Rapaić, and V. Turkulov (2023). “A unified framework for robust stability analysis of linear irrational systems in the parametric space”. In: Automatica. Second version submitted. url: https://hal.archives-ouvertes.fr/hal-03646956/.

Uses of methods with result verification for dealing with uncertainty during MIMO modeling and simulation process

For over half a century, methods with result verification have been (and are still being) successfully applied in a variety of contexts, for example, in such heterogeneous areas as robotics, computer graphics, or automated theorem proving. The use of these techniques can help, on the one hand, to verify the result of a computer simulation and, on the other hand, to deal with the bounded (epistemic) uncertainty present in the considered system in a deterministic way. Until now, modeling and simulation of multiple-input multiple-output (MIMO) systems has not received much attention from this angle, despite the fact that the whole process is influenced by uncertainty from multiple sources. Nowadays, multiplying the capacity of communication links by using the MIMO mechanism is an essential part of various wireless standards.
In this talk, we outline the stages of a MIMO modeling and simulation process and point out the sources of uncertainty along with the ways methods with result verification (in particular, interval analysis) can help to deal with them. After that, we focus on the interference suppression and resources' allocation stages with respect to the criterion of bit error ratio under good and poor scattering conditions, illustrated by a close-to-life simulation example.

A Geometric Approach to the Coverage Measure of the Area Explored by a Robot

Full coverage of an area of interest is a common task for an autonomous robot. Estimating the area explored by the robot is indeed essential for determining if path-planning algorithms lead to complete coverage. In this presentation, using a set membership approach, we propose a method for a guaranteed estimation of the area explored by an autonomous robot. The proposed algorithm is able to determine how many times each portion of the space has been sensed by the robot using a novel approach based on topological properties of the environment that has been scanned, and more precisely an estimation of certain winding numbers. This property is useful for localization inside homogeneous environments, e.g. the underwater environment, and assessment for potential revisiting missions. We demonstrate the efficiency of the presented approach on a real dataset acquired by an autonomous underwater robot.

Observer Design for a Class of Uncertain Nonlinear Systems with Sampled Outputs: Application to the Estimation of Reaction Heat in Chemical Reactors

A continuous-discrete time observer is proposed for a class of uncertain nonlinear systems where the output is available only at non uniformly spaced sampling instants. The underlying correction term depends on the output observation error and is updated in a mixed continuous-discrete fashion. The proposed observer is first introduced under a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. In the free uncertainties case, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. Moreover, to cope with the peaking phenomenon occurring during the transient periods, an improved non-peaking high gain observer is proposed. The ability of the proposed observers to perform a suitable estimation of the reaction heat in chemical reactors is highlighted through a simulation study dealing with an exothermic reaction.

Robust Fault Detection Using Set-Based Approaches for LPV Systems: Application to Autonomous Vehicles

This presentation addresses the problem of robust fault detection for Linear Parameter Varying (LPV) systems using set-based approaches. Two approaches are proposed, based respectively on set-based state and parameter estimation methods, for implementing direct and inverse test for robust fault detection (FD). The uncertainties are assumed to be unknown but bounded and their effect is propagated using zonotopic sets. These robust FD test methods aim at checking the consistency between the measured and estimated behaviour obtained from estimator in the parameter or output space considering the effect of the uncertainty. When an inconsistency is detected, a fault can be indicated. A case study based on an autonomous vehicle is employed to compare the performance of proposed FD tests.

References

Fang, X., Puig, V., Zhang, S. Fault Diagnosis and Prognosis Using a Hybrid Approach Combining Structural Analysis and Data-Driven Techniques. 5th IEEE International Conference on Control and Fault-Tolerant Systems (Systol'2021). Saint-Raphäel, France, 2021.

Zhang, S., Puig, V., Robust Fault Detection Using Set-Based Approaches. 5th IEEE International Conference on Control and Fault-Tolerant Systems (Systol'2021). Saint-Raphäel, France, 2021.

Zhang, S., Puig, V., Robust Fault Detection Using Set-Based Approaches for LPV Systems. 11th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes - SAFEPROCESS 2022 Pafos, Cyprus, 2022.

Set-based Multi-Sensor Data Fusion For Integrated Navigation Systems

This work introduces a novel set-based multi-sensor data fusion algorithm for combining aircraft 3D position estimates provided by three separate positioning systems: Inertial Reference System (IRS), Global Positioning System (GPS) and Instrument Landing System (ILS). An Extended Zonotopic Kalman Filter (EZKF) is proposed to solve the problem of IRS/GPS/ILS data fusion that rigorously encloses the nonlinearities of ILS measurement equations. Moreover, an adaptive tuning of the overall data fusion filter relies on a lower layer integrating a bank of elementary filters. The latters result from the simplification of first-order zonotopic Kalman filters optimizing a 1-norm accuracy criterion. Simulations using real flight data provided by Airbus illustrate the effectiveness of the proposed method.

Reference

S. Ifqir, C. Combastel, and A. Zolghadri. "Set-based Multi-Sensor Data Fusion For Integrated Navigation Systems." Proc. of the 5th International Conference on Control and Fault-Tolerant Systems (SysTol), 2021. (https://doi.org/10.1109/SysTol52990.2021.9596031)

Event-Triggered Interval Observers Design for Continuous-Time Linear Systems: $L_1$ - Gain Approach

This work introduces a new approach based on an event-triggered mechanism to design finite-gain L_1 interval observers for linear continuous-time systems in the presence of unknown-but-bounded uncertainties with a priori known bounds on state disturbances and measurement noises. In this setting, measurements are aperiodically sampled in order to reduce online communication between the sensors and the estimation algorithm. The proposed event-triggered mechanism relies on a dynamic condition that depends on the width of the feasible domain of the system’s uncertainties and the width of the estimated state enclosures. Moreover, the proposed approach guarantees the existence of a positive lower bound on the inter-event times, which avoids the Zeno phenomenon. On the other hand, although the sensor data are used in an irregular sampling way, the L_1-stability performance of the estimation error is satisfied.

Reference

D. Rabehi, N. Meslem, N. Ramdani. Finite-Gain L1 Event-Triggered Interval Observers Design for Continuous-Time Linear Systems. International Journal of Robust and Nonlinear Control, 2021. (https://doi.org/10.1002/rnc.5463) 

Comparison of Stochastic and Interval-Based Modeling Approaches for the Online Optimization of the Fuel Efficiency of SOFC Systems

The dynamic operation of high-temperature fuel cells under temporally varying electric loads requires models for the electric stack power that depend on the supplied fuel mass flow, the electric current, the temperature of the supplied reaction media, and the stack temperature. This information is required to optimize the fuel consumption when tracking time-varying power profiles under the constraint of preventing fuel starvation. For that reason, the stack current needs to stay below the one that defines the maximum power point. However, due to the numerous influence factors, this point is only imperfectly known so that an online estimation with a corresponding quantification of the accuracy is necessary. In this presentation, stochastic and interval-based modeling procedures are compared for an online control optimization on the basis of an experimentally validated dynamic SOFC model. The interval-based modeling combines nonlinear autoregressive models with a set-valued uncertainty quantification in a novel way.

Reference

A. Rauh, E. Auer: Comparison of Stochastic and Interval-Based Modeling Approaches for the Online optimization of the Fuel Efficiency of SOFC Systems. In Proc. of the 9th International Conference on Systems and Control (ICSC), Caen, France, 2021 (http://dx.doi.org/10.1109/ICSC50472.2021.9666656)

Reconciling Formal Methods with Metrology - Improving Verification Verdicts of Traditional Hybrid Automata

Various flavours of hybrid automata have been suggested as a formal model accurately capturing the dynamics of cyber-physical systems (CPSes) and thus facilitating exhaustive behavioural analysis thereof. In this talk, we argue that traditional hybrid automata models - including their most expressive stochastic variants - fall short of accurately capturing the behaviour of such CPSes which are inherently subject to imperfect and incomplete information due to an environment which usually is partially observed by error-afflicted sensors only. We identify inaptness to accurately represent rational decision making under uncertain information as implemented in well-engineered systems as the cause of this deficiency.

Such rational decision making is based upon and thus requires manipulation of state estimates derived from measurements. This, in turn, requires that state estimates are explicitly part of the state space both in our formal behavioural models and their reflection in verification tools. We therefore suggest a corresponding extension of hybrid automata comprising state distributions as first-class members of their state space and allowing for rational, i.e., evidence-based, decision making.

References

https://doi.org/10.1007/978-3-030-01461-2_9
https://doi.org/10.1007/978-3-030-61467-6_17

Interval Estimator Design for LPV Systems with an Extension to SEIR Epidemic Models using Observability Matrix

A new method to design interval estimators for LPV and SEIR models subject to disturbances and measurement noise is proposed. The proposed method is designed using the observability matrix and interval analysis to avoid the strict cooperativity assumptions and transformations of coordinates, therefore, it is less restrictive and more simple. The designed method saves computational time and is more accurate. The finite-time convergence is provided to show the boundedness of the interval vector and error dynamics. Two numerical examples illustrate the accuracy and high potential of the proposed technique.

References

https://doi.org/10.1016/j.jfranklin.2021.01.041

https://doi.org/10.1109/TCSII.2021.3057107

https://doi.org/10.1109/JSEN.2020.2972315

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes

Set-based estimation consists in computing enclosures of the possible system states in each time step considering bounded uncertainties and available measurement. Most of the existing zonotope methods for nonlinear state estimation employ a standard prediction-update framework with set-based prediction step, while the update step relies on conservative intersection with strips. Hence, achieving accurate enclosures using zonotopes for nonlinear discrete-time systems remains a significant challenge.

In this talk, we will discuss methods that outer approximate the propagation of constrained zonotopes (CZs) through nonlinear mappings, allowing for state estimation of nonlinear discrete-time systems using CZs. Unlike zonotopes, CZs are closed under the intersection operation and are capable of describing asymmetric convex polytopes. Algorithms for the update step are also presented considering nonlinear measurement. The discussed methods also improve the standard prediction-update framework for systems with invariants by adding a consistency step considering nonlinear equality constraints.

References

https://doi.org/10.1016/j.automatica.2019.108614
https://doi.org/10.1016/j.automatica.2021.109638

Global optimization and interval constraint programming using Julia: Symbolics, code generation and GPUs

I will present an overview of an integrated tooling pipeline for global optimization and interval constraint programming using the Julia language. 

By integrating with the extensive ecosystem of other packages in Julia, we can interactively specify a symbolic description of a constrained optimization problem, perform code generation of efficient contractors for interval constraint propagation, run the code on the GPU, and visualize the results.

References

Open-source packages: https://github.com/JuliaIntervals

Overview and documentation: https://juliaintervals.github.io/

Guaranteed Nonlinear Model Predictive Control based on Validated Simulation

In this talk, we will develop a new validated and reliable nonlinear model predictive control (NMPC), specifically formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). First, all the dynamic parameters will be identified in a guaranteed way considering various uncertainties on the embedded sensors and the system’s design. Hence the guaranteed identification is based on interval analysis and set-inversion tools to determine inertial and frictional parameters in a complete and validated way. Secondly, a new reliable NMPC strategy is designed to consider different constraints crucial for the system’s safety and stability, namely the state and the control limits. The proposed controller encompasses two steps: filtering and branching procedures, enabling finding the input intervals that fulfill the state constraints and ensuring the convergence to the reference interval. Then, the optimization procedure allows computing the sub-optimal and punctual control input to stabilize the dynamic system. The proposed algorithms are investigated through several simulations using the DynIbex library and many experiments via a nonlinear inverted pendulum.

References

1. M. Fnadi, J. Alexandre dit Sandretto, G. Ballet and L. Fribourg. Guaranteed Identification of Viscous Friction for a Nonlinear Inverted Pendulum Through Interval Analysis and Set Inversion. 2021 American Control Conference (ACC), 2021, 3920-3926. DOI: 10.23919/acc50511.2021.9483185
   
2. M. Fnadi, J. Alexandre dit Sandretto. Experimental Validation of a Guaranteed Nonlinear Model Predictive Control. In Algorithms, 2021, 14, 248. DOI: 10.3390/a14080248
   

Enclosing vs. Non-enclosing Measurements in Interval Data Processing

Since the 1960s, Interval Analysis has been successfully used to process data with so-called "bounded uncertainties".

These results are well published, widely known, and subsequently they took shape in a separate scientific discipline called Interval Data Analysis. On the other hand, in the late 90s of the XX century, the so-called Symbolic Data Analysis  was born, and the processing of interval data is also included in the scope of its applications. Over the past quarter

of a century, this scientific direction has also gained popularity and recognition. But what is the relationship between

Interval Data Analysis and Symbolic Data Analysis? When should we apply one approach and when the other? The talk is

devoted to answering these questions.

One of the by-products of the undertaken research is the introduction of a fundamental definition of "enclosing" (covering)  and "non-enclosing" (non-covering) interval measurement (observation). It helps  not only to understand the difference  between Interval Data Analysis and Symbolic Data Analysis, but better highlights the role and place of interval analysis  methods in data processing.

Affine Iterations and Wrapping Effect: an Approach Based on the SVD

Affine iterations of the form x_n+1 = Ax_n+b converge, using real arithmetic, if ρ(A)<1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if ρ(|A|) >1. We will recall some results due to Mayer and co-authors regarding the divergence of the iterates. Then, we will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x₀ and b are intervals, and we will propose a new approach based on the SVD decomposition of A. We will compare, both theoretically and experimentally, the widths of the iterates computed by different methods: the naive iteration, Lohner's QR-factorization method and our method. Our method is computationally less demanding and gives good results when some quantity is not too large.

Enclosing Optimal Trajectories Using Spatio-Temporal Constrained Zonotopes

We consider an optimal control problem subject to bounded uncertainties on parameters and initial state. Our goal is to enclose all optimal trajectories. First, optimal trajectories are characterized as solutions of an uncontrolled switched system subject to boundary constraints. Then, we propose an approach based on validated simulation tweaked with spatio-temporal constrained zonotopes to enclose the solutions of this system. This approach propagates boundary constraints backward with no hindrance from variable switch times.

Reference

Etienne Bertin, Elliot Brendel, Bruno Hérissé, Julien Alexandre Dit Sandretto, Alexandre Chapoutot. Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics. Acta Cybernetica, University of Szeged, Institute of Informatics, 2021, pp.1-25. https://doi.org/10.14232/actacyb.285798

Interval Methods for Solving Quantified Nonlinear Problems for Control Engineering and Machine Learning

It is well-known that interval methods can be used for solving optimization problems or systems of nonlinear equations. In the paper, other examples of problems formulated using logical formulae (some of them with quantifiers) will be given.
A generic algorithm for solving them will be presented, based on the author's earlier considerations. Specific examples related to control theory and machine learning are going to
be considered.

References

[1] B. J. Kubica, A class of problems that can be solved using interval algorithms, SCAN 2010, Computing, Vol. 94 (2-4), pp. 271 – 280 (2012). DOI: 10.1007/s00607-011-0173-9.
[2] B. J. Kubica, P. Hoser, A. Wiliński, Interval methods for seeking fixed points of recurrent neural networks. In:  International Conference on Computational Science (pp. 414-423), Springer, Cham. DOI: 10.1007/978-3-030-50420-5_30.
[3] B. J. Kubica, Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems,
ISBN 978-3-030-13795-3, Springer, 2019. DOI: 10.1007/978-3-030-13795-3.

Interval Observer Design for Uncertain Discrete-Time Linear Switched Systems with Unknown Inputs

This presentation deals with unknown input interval observers for discrete-time linear switched systems. Two structures are used. The first one is classical and based on a coordinate transformation. The second structure is introduced to overcome the design difficulty of the classical approach. The interval observer gains are computed by solving Linear Matrix Inequalities (LMIs) derived from multiple quadratic Lyapunov functions (MQLF) under average dwell time switching signals.

Reference

Marouani, G., Dinh, T. N., Raïssi, T., Wang, X., Messaoud, H.: Unknown input interval observers for discrete-time linear switched systems. European Journal of Control, 59, 165-174. 2021. DOI: https://dx.doi.org/10.1016/j.ejcon.2020.09.004

A Modified Twin Arithmetic to Characterize Uncertain Sets

Given an interval [a,b]. When the bounds a and b are not known exactly, then the interval becomes uncertain. When this uncertainty is represented by an interval for the bounds (i.e., a in [a] and b in [b]), then the corresponding set of intervals is called a 'twin'. More precisely, a twin [[x]] is the set of all intervals [x]=[a,b] such that a in [a] and b in [b].

A 'thick set' [[X]] with bounds A and B is a set of all subsets X of R^n such that A is a subset of X which is a subset of B. Thick sets occur naturally in several applications such as in robotics when we want to characterize the zone that has been explored by a robot when the trajectory of the robot is uncertain (for instance represented by a tube). Whereas a twin can be interpreted as an uncertain set of R, a thick set can thus be understood as an uncertain set of R^n.

In this talk, I will show that a modified twin arithmetic will allow us to characterize efficiently thick sets. Some applications related to robotics exploration will be given.

Biography 

Thomas Chevet obtained his engineering degree and his PhD in Automatic Control in 2017 from Supélec and in 2020 from Université Paris-Saclay, respectively. Currently, he is a Postdoctoral Researcher at ONERA, the French Aerospace Lab. His research interests focus on interval observers, fault tolerant control, prognostics and health management, and model predictive control..

Interval Observers for Fault Detection and Estimation

This talk deals with the use of new interval observers for fault detection and joint estimation of state and unknown inputs for linear systems subject to bounded perturbations and measurement noise. First, we present a robust interval observer for a continuous-time linear parameter-varying (LPV) system with unknown and unmeasurable parameter. This observer is used for sensor fault detection. Then, we will study joint estimation of both the state and unknown inputs of discrete-time linear time-invariant (LTI)/LPV systems. To do so, we design a zonotopic observer for a discrete-time LTI system and an interval observer for a discrete-time LPV system, both with unknown and unmeasurable parameter vector. These estimation methods are based on the introduction of additional weighting matrices to help attenuate the effect of the system's uncertainties and ensure the stability and cooperativity of the interval observers. The algorithms are tested on simulation examples to show their efficiency.

References

T. Chevet, T.N. Dinh, J. Marzat, Z. Wang, and T. Raïssi. "Zonotopic Kalman Filter-Based Interval Estimation for Discrete-Time Linear Systems With Unknown Inputs." IEEE Control Systems Letters, 6 (2022): 806-811. DOI: https://dx.doi.org/10.1109/LCSYS.2021.3086562

T. Chevet, T.N. Dinh, J. Marzat, and T. Raïssi. "Interval Estimation for Discrete-Time Linear Parameter-Varying System with Unknown Inputs." 60th IEEE Conference on Decision and Control, Austin, TX, USA, 2021. Accepted.

T. Chevet, T.N. Dinh, J. Marzat, and T. Raïssi. "Robust Sensor Fault Detection for Linear Parameter-Varying Systems using Interval Observer." Proceedings of the 31st European Safety and Reliability Conference, Angers, France, pp. 1486-1493, 2021. DOI: https://dx.doi.org/10.3850/978-981-18-2016-8_380-cd

Biography 

Quoc Hung Lu received his Bachelor in Mathematics from the University of Sciences of Hochiminh City, Vietnam, in 2016, then his Master degree in Applied Mathematics from the University of Toulouse III - Paul Sabatier in 2018. Currently, he is working as a PhD student at LAAS-CNRS (2018-2022). His research interests focus on Kalman filtering and extensions, FDI, Active Diagnosis, Optimization and Applied Probability and Statistics (in related fields of research).

Interval Kalman Filter Enhanced by Lowering the Covariance Matrix Upper Bound

In this talk, a variance upper bound based interval Kalman filter is proposed. This fillter enhances the interval Kalman filter of the same principle proposed in [Tran et al., 2017] for uncertain discrete-time linear models. The systems under consideration are subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of the Gaussian noises. Using the spectral decomposition of a symmetric matrix and by optimizing the gain matrix of the proposed filter, we achieve to lower the minimal upper bound on the state estimation error covariance for all admissible uncertainties. An improved algorithm providing a less conservative error covariance upper bound than the approach proposed in [Tran et al., 2017] is also proposed. The state estimation is determined using interval analysis in order to enclose the set of all possible solutions of the classical Kalman filter consistent with the uncertainties.

References

[Tran et al., 2017] T.A. Tran, C. Jauberthie, F. Le Gall, and L. Travé-Massuyès: Interval Kalman Filter Enhanced by Positive Definite Upper Bounds. In Proceedings of the
20th IFAC World Congress, Toulouse, France, 2017. DOI: 10.1016/j.ifacol.2017.08.315

Q. Lu, S. Fergani, C. Jauberthie and F. Le Gall, Optimally bounded Interval Kalman Filter, 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp. 379-384,
DOI: 10.1109/CDC40024.2019.9028918.

Q. Lu, F. Soheib, and C. Jauberthie, A New Scheme for Fault Detection Based on Optimal Upper Bounded Interval Kalman Filter, 19th IFAC Symposium on System Identification (At: virtual), July 2021

Biography 

Simon Rohou is Associate Professor at ENSTA Bretagne (Lab-STICC, Brest, France). He defended a Franco-British PhD in Robotics (ENSTA Bretagne, University of Sheffield), in 2017. He was a Postdoctoral Researcher on constraint propagation techniques for dynamical systems at IMT Atlantique (LS2N, Nantes, France). His work focuses on robotics and especially set-membership localization methods for autonomous underwater robots. His research interests include constraint propagation and interval methods for state estimation.

Interval State Estimation by Solving Data Association

In this talk, we will estimate the set of feasible trajectories of an underwater vehicle. The robot does not know its initial position, but measures its velocity and heading. In addition, it is able to perceive rocks on the seabed, and is endowed with a map of these landmarks. It is however impossible to distinguish a rock from another, due to their shape and sonar uncertainties. Yet, an identification of the rocks is necessary in order to localize the vehicle. This amounts to a data association problem, where each node of the map must be associated with the perceived landmarks. This problem will be solved simultaneously with state estimation, without image processing. Indeed, any state information may help to associate observations with nodes of the map. Valid and reliable associations are then useful to improve state estimation, which could allow further associations. This chicken-and-egg problem will be solved with guaranteed outputs, by using intervals, tubes and contracting operators on non-linear differential equations and discrete constraints. We will see how this can be dealt with by Constraint Propagation and implemented using simple tools such as those of the Codac library (http://codac.io).

References

Simon Rohou, Benoît Desrochers, Luc Jaulin: Set-membership state estimation by solving data association, IEEE International Conference on Robotics and Automation (ICRA), 2020.

DOI: 10.1109/ICRA40945.2020.9197039

Simon Rohou, Luc Jaulin, Lyudmila Mihaylova, Fabrice Le Bars, Sandor M. Veres: Reliable robot localization: a constraint-programming approach over dynamical systems, ISTE Group, 2019. DOI: 10.1002/9781119680970

Biography 

Amine Abadi holds a doctorate degree in electrical engineering from the University of Sousse and a doctorate degree in industrial sciences and techniques at THE UNIVERSITY OF ORLÉANS. My current research focuses on creating autonomous guidance laws for robotic systems in the presence of uncertain parameters, external disturbances and measurement noise. I work mainly on flatness control, sliding mode control, extended state observer, interval observers, and machine learning control, with applications to autonomous robotics.

Guaranteed Tracking Controller for Wheeled Mobile Robots Based on Flatness and Interval Observer

This paper proposes a guaranteed tracking controller for a Wheeled Mobile Robot (WMR) based on the differential flatness theory and the interval observer. Using the flatness property, it is possible to transform the nonlinear WMR model into a canonical Brunovsky form, for which it is easier to create a state feedback controller. Since, in most real applications, the WMR is subjected to uncertainties such as slip, disturbance and noise, control algorithms must be modified to take into account those uncertainties. Therefore, based on the information of the upper and lower limits of the initial condition and all the uncertainties, an interval observer that generates an envelope enclosing every feasible state trajectory is developed. After that, based on the center of the obtained interval observer, a new control law is proposed to guarantee the tracking performance of the WMR despite the existence of un-measurable states and bounded uncertainties. The closed loop stability of the system is proven analytically using the Lyapunov theorem. A lot of numerical simulations are realized in order to demonstrate the efficiency of the suggested guaranteed tracking control scheme.

References

https://doi.org/10.1109/CDC40024.2019.9029479

https://doi.org/10.1080/00207179.2019.1610903

Biography 

Pierre-Jean Meyer is a research fellow at the ESTAS lab of Université Gustave Eiffel in Lille, France. He received a PhD in Automatic Control from Université Grenoble Alpes, France, in 2015. He was a postdoctoral researcher at KTH Royal Institute of Technology in Stockholm between 2015 and 2017, and at University of California, Berkeley between 2017 and 2020. His research interests include reachability analysis and abstraction-based control synthesis.

Interval Reachability Analysis

In this talk, I will give an overview of several methods using intervals to over-approximate the finite-time reachable set of both continuous-time and discrete-time systems. Similarly to the content of the recently published book "Interval Reachability Analysis", we will cover methods relying on the monotonicity property and its generalizations, bounds on the contraction or growth between any pair of system trajectories, or sampling-based approaches. We will propose a more tutorial-like presentation of these methods, shifting the focus on the intuition, requirements and use of each method, rather than technical details and proofs. The talk will conclude with an overview of the Matlab library "TIRA: Toolbox for Interval Reachability Analysis" offering a unified implementation of most of the presented approaches.

References

Pierre-Jean Meyer, Alex Devonport and Murat Arcak, "Interval Reachability Analysis: Bounding Trajectories of Uncertain Systems with Boxes for Control and Verification". Springer Briefs in Control, Automation and Robotics, 2021. https://doi.org/10.1007/978-3-030-65110-7
Pierre-Jean Meyer, Alex Devonport and Murat Arcak, "TIRA: Toolbox for Interval Reachability Analysis". 22nd ACM International Conference on Hybrid Systems: Computation and Control, p. 224-229, 2019. https://doi.org/10.1145/3302504.3311808
"TIRA: Toolbox for Interval Reachability Analysis": https://gitlab.com/pj_meyer/TIRA

Biography 

Alex dos Reis de Souza graduated from the Federal University of Uberlândia (UFU, Brazil) as a Mechatronics Engineer in 2018. Currently, he is a PhD candidate at Inria - Lille Nord Europe, as a part of the Valse team. His research interests include nonlinear and robust control, robust estimation, and model predictive control.

Robust Output Feedback MPC via Interval Observers

Reference

A. R. de Souza, D. Efimov, T. Raïssi and X. Ping, "Robust Output Feedback MPC: An Interval-Observer Approach," 2020 59th IEEE Conference on Decision and Control (CDC), 2020, pp. 2529-2534, DOI: 10.1109/CDC42340.2020.9304070.

Biography 

Wentao Tang received his Bachelor’s Degree of Science from Harbin Institute of Technology, Harbin, China, in 2015. He was a visiting Ph.D. student at INRIA, Rennes, France, for one year from 2019. He is currently a Ph.D. candidate with the Department of Control Science and Engineering at Harbin Institute of Technology. His research interests include set-membership estimation and fault diagnosis.

Set-Membership Estimation for Discrete-Time Systems: The Two-Step Method

References

W. Tang, Z. Wang, Y. Wang, T. Raissi, & Y. Shen. Interval estimation methods for discrete-time linear time-invariant systems. IEEE Transactions on Automatic Control, 2019, 64(11):4717-4724. (http://dx.doi.org/10.1109/TAC.2019.2902673)

W. Tang, Z. Wang, & Y. Shen. Interval estimation for discrete-time linear systems: A two-step method. Systems & Control Letters, 2019, 123:69-74. (http://dx.doi.org/10.1016/j.sysconle.2018.11.001)

Biography 

Daniel Wilczak is a professor of Computer Science at the Jagiellonian University (Kraków) in Poland. He obtained his Ph.D. in Computer Science from the Jagiellonian University in 2003 under the supervision of Marian Mrozek. From 2008 to 2010 he was a member of CAPA research group led by Warwick Tucker at the University of Bergen (Norway) and then at Uppsala University (Sweden). In 2011, he obtained his habilitation in Computer Science. He is one of the main developers of the CAPD library — a C++ toolbox for rigorous numerical analysis of dynamical systems. His research interests concentrate around rigorous numerical analysis of finite and infinite dimensional dynamical systems including both theoretical and numerical aspects.

Validated Integration of Variational Equations for ODEs and Applications

References

[1] CAPD::DynSys Computer Assisted Proofs in Dynamics, a C++ package for rigorous numerics. http://capd.ii.uj.edu.pl/
[2] T. Kapela, M. Mrozek, D. Wilczak, P Zgliczyński, CAPD::DynSys: A Flexible C++ Toolbox for Rigorous Numerical Analysis of Dynamical systems, Communications in Nonlinear Science and Numerical Simulation, https://doi.org/10.1016/j.cnsns.2020.105578
[3] T. Kapela, D. Wilczak, P Zgliczyński, Recent Advances in Rigorous Computation of Poincaré Maps, Communications in Nonlinear Science and Numerical Simulation, under review 
[4] P. Zgliczyński, C^{^}-Lohner Algorithm, Found. Comp. Math., https://doi.org/10.1007/s102080010025 
[5] I. Walawska, D. Wilczak, An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs, Applied Mathematics and Computation, https://doi.org/10.1016/j.amc.2016.07.005

For a related tutorial on Computer Assisted Proofs in Dynamics, please have a look at Daniel's personal web page: ww2.ii.uj.edu.pl/~wilczak/

Biography 

Sergey was born on Nov. 27, 1941. He graduated from the Ural Federal University (1964) as a radio-engineer and as an application mathematician (1970, both, in Ekaterinburg), Phd on aircraft automatic control from the Academy of Civil Aviation (1977, Sankt-Petersburg). Now, he works as a Senior Scientific Researcher at the N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences and in the Ural Federal University (IRIT-RTF) as an Associate Prof., as a Lecturer, and Tutor.

Interval Methods for Processing Noised Data From Several Information Sources

References

S.I. Kumkov. SWIM'2015: An Estimation Problem of Chemical Process with Confluent Parameters: An Interval Approach, Reliable Computing

S.I. Kumkov, Yu. V. Mikushina. Interval Approach to Identification of Catalytic Process Parameters, Reliable Computing

https://doi.org/10.1007/s11581-015-1592-y

https://doi.org/10.1109/SMC.2017.8122631

Remark

The article quoted by S.P. Shary can be found here: Link
In his question, he referred to p. 25, where the notion of "enclosing/covering measurements" is given and visualized.

Biography 

Naima Sehli obtained her engineering degree in industrial computing and automation in 2016 from the National Institute of Applied Science and Technology. She is currently preparing her PhD thesis between the National Engineering School of Tunis and the Conservatoire National des Arts et Métiers. Her research interests include fault detection and diagnosis for time-delay systems.

Interval Estimation for Linear Discrete-Time Delay Systems

Reference

Naima Sehli, Zhenhua Wang, Kaouther Ibn Taarit, Tarek Raïssi, and Moufida Ksouri. "Interval estimation for linear discrete-time delay systems". In 21st IFAC World Congress, July 2020.

Biography 

Ziyun Wang received his PhD degree in control science and engineering from Jiangnan University, Wuxi, China, in 2015. He was a visiting scholar with Louisiana State University, USA, from 2014 to 2015 and with Yeungnam University, Republic of Korea, in 2019. He is currently an associate professor with the College of Internet of Things Engineering, Jiangnan University. His research interests include filtering methods and their applications in fault diagnosis, system identification and state estimation.

Vector Set Inversion Interval Filtering Based Fault Observer Design

In this presentation, a vector set inversion interval filtering based actuator fault observer design method is studied. The main contribution of this short talk is to design a fault observer, to obtain the interval estimation of actuator fault. The set inversion is carried out by using the multi-time measurement outputs. Inversion contraction interval can be used to improve the observer estimation interval by intersecting both intervals, which reduces the wrapping effect of interval computation.

References

http://doi.org/10.1049/iet-cta.2019.1229

http://doi.org/10.1016/j.jfranklin.2020.02.041

Biography 

Bernd Tibken received his Diploma degree in Physics from the University of Hamburg, Hamburg, Germany, in 1985, his

Ph.D. degree from the Technical University of Hamburg, Harburg, Germany, in 1990, and his Habilitation degree from the University of Ulm, Germany, in 1996. Since 1999 he has been Full Professor of Automatic Control with the Faculty of Electrical, Information, and Media Engineering at the University of Wuppertal, Germany.

Observability of Nonlinear Systems and Injectivity

In this presentation, the observability of nonlinear systems is investigated. Using Lie series, the observability question is transformed into the test of injectivity for the observability mapping.

The main contribution of this short talk is an interval condition to test injectivity of a function on an interval vector. This condition will be used in Thomas Paradowski's subsequent contribution in which an algorithm for testing observability is presented.

Biography 

Thomas Paradowski studied in the Bachelor's and Master's programs of Electrical Engineering at the University of Wuppertal, Germany, from 2007 to 2014. Since 2014, he has been a research assistant at the Chair of Automation and Control Theory at the University of Wuppertal under the supervision of Prof. Tibken, where he completed his Ph.D. dissertation in April 2020 and continued working at the same institute.

Observability of Uncertain Nonlinear Systems Using Interval Analysis

The use of state controllers requires the implementation of observers. Before such an observer can be designed it is necessary to verify that the system is observable. Unfortunately in case of nonlinear systems it is very difficult to check the observability. Even for local observability, the observability rank condition only provides a sufficient condition. Verifying the global observability is significantly more challenging. In this talk, we will show a method based on interval arithmetics and an automated computation of the Lie-derivatives to verify the global observability of nonlinear systems. Furthermore, the benefits of this method go beyond the mere determination of observability. Thus, those states can be identified which are globally observable on a given interval and which are not. In case the nonlinear system is not observable, those states can be identified which cannot be distinguished to a given set with the output behavior. This makes it possible to draw conclusions on how to influence the output function, and thus the choice of the sensors, in order to achieve the desired observability.

References

https://doi.org/10.3390/a13030066

https://dx.doi.org/10.23919/ACC.2017.7963557

Vulnerability Analysis and Attack Detection for Cyber-Physical Systems: A Zonotopic Approach

This talk is concerned with the security of a Cyber-Physical System (CPS). First, we analyze the CPS vulnerability against stealthy attacks. We quantify the potential impact of stealthy attacks on system state using zonotopes. A CPS is strictly vulnerable if the attack induced zonotope of state is unbounded. A CPS is safe if the attack induced zonotope of state is enclosed by the safety region. Otherwise, the CPS is vulnerable and the vulnerability metric is characterized using one-sided Hausdorff distance. Second, we consider attack detection based on zonotopic reachability analysis. A false data injection attack is detected if there is no intersection between the predicted state set and the measurement state set. These sets are online calculated via zonotopic segments minimization. Two approaches, namely, projection and polytopic conversion, are presented to check the intersection situation. The detection performance is quantified using the stealthy attack set. Further, we consider replay attacks. To detect a replay attack, a watermark signal based active detection mechanism is introduced. Numerical simulations are conducted to demonstrate the validity of the proposed method.

Fractional-Order System Models and Their Verified Numerical Analysis Using Interval Methods

Verified integration of initial value problems for sets of ordinary differential equations were investigated in many research projects and resulted in numerous software implementations over the last decades. However, ordinary differential equations with integer orders of the derivatives are not the only relevant dynamic system models in modeling dynamic systems in engineering as well as computational physics, biology and other disciplines. One of the emerging modeling assumptions studied over the recent years is the use of fractional-order models that are characterized by non-integer order temporal derivatives. This presentation briefly touches upon their use in modeling applications from the areas of robotics and energy systems as well as for describing dynamic elements that are useful for so-called loop shaping techniques in control design. Novel, interval-based simulation routines for fractional-order systems are presented with an illustrating example from the field of modeling Lithium-ion batteries.

References

https://doi.org/10.14232/actacyb.285660

http://dx.doi.org/10.4204/EPTCS.331.2

Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries

A Boundary Approach for Set Inversion

A set defined as a set-inversion problem X=f^-1(Y) has an inside and an outside, which may be possibly empty. When we characterize the solution set X using contractors, existing techniques generally perform the same computation twice: once for the inside of X and once for the outside. The factorization of the calculus is generally not proposed to keep the solver simple and generic. A simple way to factorize the computation is to inverse the boundary of Y only. We thus get a characterization of the boundary of X. Unfortunately, for each box of the generated paving, we lose the information on which side of the boundary the box is. In this talk, I will explain how this information can be obtained during the propagation process at a negligible cost. For this purpose, I will introduce the notions of directional contractors and contractible functions. These tools will also be used to derive contractor techniques that can be more efficient than existing ones.

December 04, 2020

December 04, 2020

References

https://doi.org/10.1016/j.ifacol.2019.06.109

https://doi.org/10.1109/PC.2019.8815052