Numerical Computation of Control Lyapunov Functions in the Sense of Generalized Gradients

Abstract : The existence of a control Lyapunov function with the weak infinitesimal decrease via the Dini or the proximal subdifferential and the lower Hamiltonian characterizes asymp-totic controllability of nonlinear control systems and differential inclusions. We study the class of nonlinear differential inclusions with a right-hand side formed by the convex hull of active C 2 functions which are defined on subregions of the domain. For a simplicial triangulation we parametrize a control Lyapunov function (clf) for nonlinear control systems by a continuous, piecewise affine (CPA) function via its values at the nodes and demand a suitable negative upper bound in the weak decrease condition on all vertices of all simplices. Applying estimates of the proximal subdifferential via active gradients we can set up a mixed integer linear problem (MILP) with inequalities at the nodes of the triangulation which can be solved to obtain a CPA function. The computed function is a clf for the nonlinear control system. We compare this novel approach with the one applied to compute Lyapunov functions for strongly asymptotically stable differential inclusions and give a first numerical example.
Type de document :
Communication dans un congrès
MTNS 2014, 2014, Groningen, Netherlands. pp.1173-1180, Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. 〈https://fwn06.housing.rug.nl/mtns2014/〉
Liste complète des métadonnées

Littérature citée [16 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01098270
Contributeur : Estelle Bouzat <>
Soumis le : mardi 23 décembre 2014 - 15:24:39
Dernière modification le : vendredi 13 octobre 2017 - 17:08:16
Document(s) archivé(s) le : mardi 24 mars 2015 - 10:40:41

Fichier

baier_et_al_clf_2014.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01098270, version 1

Collections

Citation

Robert Baier, Sigurđur Freyr Hafstein. Numerical Computation of Control Lyapunov Functions in the Sense of Generalized Gradients. MTNS 2014, 2014, Groningen, Netherlands. pp.1173-1180, Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. 〈https://fwn06.housing.rug.nl/mtns2014/〉. 〈hal-01098270〉

Partager

Métriques

Consultations de la notice

172

Téléchargements de fichiers

75