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Numerical computation of control Lyapunov functions in the sense of generalized gradients

Titelangaben

Baier, Robert ; Hafstein, Sigurdur Freyr:
Numerical computation of control Lyapunov functions in the sense of generalized gradients.
In: MTNS 2014 : 21st International Symposium on Mathematical Theory of Networks and Systems, July 7-11, 2014, Groningen, The Netherlands ; Proceedings. - Groningen : University of Groningen , 2014 . - S. 1173-1180
ISBN 978-90-367-6321-9

Dies ist die aktuelle Version des Eintrags.

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Link zum Volltext (externe URL): Volltext

Angaben zu Projekten

Projekttitel:
Offizieller ProjekttitelProjekt-ID
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Projektfinanzierung: Andere
European Union "FP7-People-ITN" programme

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 asymptotic 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 C² [$C^2$] 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.

Weitere Angaben

Publikationsform: Aufsatz in einem Buch
Begutachteter Beitrag: Ja
Zusätzliche Informationen: Paper No. 232, full paper.

Contents:
I. Preliminaries
II. Control Lyapunov Functions
III. Approach with Mixed Integer Programming
IV. Numerical Example
V. Conclusions

© 2014 IEEE. Reuse of this content is subject to the IEEE Copyright.
This content will be published in: Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 7–11, 2014, University of Groningen, Groningen, Netherlands, check the forthcoming abstract in IEEE Explore.
Keywords: control Lyapunov functions; asymptotic controllability; nonlinear control systems; continuous, piecewise affine functions; mixed integer linear programming
Fachklassifikationen: Mathematics Subject Classification Code: 93D30 (93B05 90C11)
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Profilfelder
Profilfelder > Advanced Fields
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 11 Mär 2015 06:37
Letzte Änderung: 23 Mär 2015 12:24
URI: https://eref.uni-bayreuth.de/id/eprint/8004

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