Surveillance préventive des systèmes hybrides à incertitudes bornées

This thesis is dedicated to the development of generic algorithms for the set-membership observation of the continuous state and the discrete mode of hybrid dynamical systems in order to achieve fault detection. This thesis is organized into two parts. In the first part, we have proposed a fast and effective method for the set-membership guard crossing. It consists in carrying out bisection in the time direction only and then makes several contractors working simultaneously to reduce the domain of state vectors located on the guard during the study time slot. Then, we proposed a method for merging trajectories based on zonotopic enclosures. These methods, used together, allowed us to characterize in a guaranteed way the set of all hybrid state trajectories generated by an uncertain hybrid dynamical system on a finite time horizon. The second part focuses on set-membership methods for the parameters or the hybrid state (mode and continuous state) of a hybrid dynamical system in a bounded error framework. We started first by describing fault detection methods for hybrid systems using the parametric approach and the hybrid observer approach. Then, we have described two methods for performing fault detection tasks. We have proposed a method for computing in a guaranteed way all the parameters consistent with the hybrid dynamical model, the actual data and the prior error bound, by using our nonlinear hybrid reachability method and an algorithm for partition which we denote SIVIA-H. Then, for hybrid state estimation, we have proposed a method based on a predictor-corrector, which is also built on top of our non-linear method for hybrid reachability.Cette thèse est dédiée au développement d’algorithmes génériques pour l’observation ensembliste de l’état continu et du mode discret des systèmes dynamiques hybrides dans le but de réaliser la détection de défauts. Cette thèse est organisée en deux grandes parties. Dans la première partie, nous avons proposé une méthode rapide et efficace pour le passage ensembliste des gardes. Elle consiste à procéder à la bissection dans la seule direction du temps et ensuite faire collaborer plusieurs contracteurs simultanément pour réduire le domaine des vecteurs d’état localisés sur la garde, durant la tranche de temps étudiée. Ensuite, nous avons proposé une méthode pour la fusion des trajectoires basée sur l'utilisation des zonotopes. Ces méthodes, utilisées conjointement, nous ont permis de caractériser de manière garantie l'ensemble des trajectoires d'état hybride engendrées par un système dynamique hybride incertain sur un horizon de temps fini. La deuxième partie de la thèse aborde les méthodes ensemblistes pour l'estimation de paramètres et pour l'estimation d'état hybride (mode et état continu) dans un contexte à erreurs bornées. Nous avons commencé en premier lieu par décrire les méthodes de détection de défauts dans les systèmes hybrides en utilisant une approche paramétrique et une approche observateur hybride. Ensuite, nous avons décrit deux méthodes permettant d’effectuer les tâches de détection de défauts. Nous avons proposé une méthode basée sur notre méthode d'atteignabilité hybride non linéaire et un algorithme de partitionnement que nous avons nommé SIVIA-H pour calculer de manière garantie l'ensemble des paramètres compatibles avec le modèle hybride, les mesures et avec les bornes d’erreurs. Ensuite, pour l'estimation d'état hybride, nous avons proposé une méthode basée sur un prédicteurcorrecteur construit au dessus de notre méthode d'atteignabilité hybride non linéaire

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

A CSP versus a zonotope-based method for solving guard set intersection in nonlinear hybrid reachability

International audienceComputing the reachable set of hybrid dynamical systems in a reliable and verified way is an important step when addressing verification or synthesis tasks. This issue is still challenging for uncertain nonlinear hybrid dynamical systems. We show in this paper how to combine a method for computing continuous transitions via interval Taylor methods and a method for computing the geometrical intersection of a flowpipe with guard sets, to build an interval method for reachability computation that can be used with truly nonlinear hybrid systems. Our method for flowpipe guard set intersection has two variants. The first one relies on interval constraint propagation for solving a constraint satisfaction problem and applies in the general case. The second one computes the intersection of a zonotope and a hyperplane and applies only when the guard sets are linear. The performance of our method is illustrated on examples involving typical hybrid systems

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications