Safety Controller Synthesis for Incrementally Stable Switched Systems Using Multiscale Symbolic Models

Abstract : We propose an approach to the synthesis of safety controllers for a class of switched systems, based on the use of multiscale symbolic models that describe transitions of various durations and whose sets of states are given by a sequence of embedded lattices approximating the state-space, the finer lattices being accessible only by transitions of shorter duration. We prove that these multiscale symbolic models are approximately bisimilar to the original switched system provided it enjoys an incremental stability property attested by the existence of a common Lyapunov function or of multiple Lyapunov functions with a minimal dwell-time. Then, for specifications given by a safety automaton, we present a controller synthesis algorithm that exploits the specificities of multiscale symbolic models. We formalize the notion of maximal lazy safety controller which gives priority to transitions of longer durations; the shorter transitions and thus the finer scales of the symbolic model are effectively explored only when safety cannot be ensured at the coarser level and fast switching is needed. We propose a synthesis algorithm where symbolic models can be computed on the fly, this allows us to keep the number of symbolic states as low as possible. We provide computational evidence that shows drastic improvements of the complexity of controller synthesis using multiscale symbolic models instead of uniform ones.
Type de document :
Article dans une revue
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (6), pp.1537-1549. 〈10.1109/TAC.2015.2478131〉
Liste complète des métadonnées

Littérature citée [22 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01197426
Contributeur : Antoine Girard <>
Soumis le : vendredi 19 février 2016 - 09:48:39
Dernière modification le : vendredi 17 février 2017 - 16:11:33
Document(s) archivé(s) le : vendredi 20 mai 2016 - 10:29:31

Fichier

multiscale-tac-double.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Antoine Girard, Gregor Gössler, Sebti Mouelhi. Safety Controller Synthesis for Incrementally Stable Switched Systems Using Multiscale Symbolic Models. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (6), pp.1537-1549. 〈10.1109/TAC.2015.2478131〉. 〈hal-01197426v2〉

Partager

Métriques

Consultations de
la notice

424

Téléchargements du document

186