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A characteristics based curse-of-dimensionality-free approach for approximating control Lyapunov functions and feedback stabilization

Titelangaben

Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:
A characteristics based curse-of-dimensionality-free approach for approximating control Lyapunov functions and feedback stabilization.
Bayreuth ; Melbourne , 2018 . - 8 S.

Volltext

Link zum Volltext (externe URL): Volltext

Angaben zu Projekten

Projekttitel:
Offizieller ProjekttitelProjekt-ID
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov FunctionsDP160102138
Ohne AngabeFA2386-16-1-4066

Projektfinanzierung: ARC (Australian Research Council)
AFOSR/AOARD

Abstract

This paper develops a curse-of-dimensionality-free numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic con- trol systems described by systems of ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinite-horizon optimal control problem. The infinite-horizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensionality, an extension of a recently developed characteristics based framework is proposed. Theoretical foundations of the developed approach are given together with practical discussions regarding its implementation, and numerical examples are also provided. In particular, it is pointed out that the curse of complexity may remain a significant issue even if the curse of dimensionality is avoided.

Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Keywords: control Lyapunov functions; optimal control; optimization; stabilization by feedback
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) > Lehrstuhl Mathematik V (Angewandte Mathematik) - Univ.-Prof. Dr. Lars Grüne
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Professur Angewandte Mathematik (Angewandte Mathematik)
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder
Profilfelder > Advanced Fields
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 17 Feb 2018 22:00
Letzte Änderung: 20 Feb 2018 09:14
URI: https://eref.uni-bayreuth.de/id/eprint/42306