Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control. Part I: Theory

Title data

Yegorov, Ivan ; Dower, Peter M. ; Grüne, Lars:
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control. Part I: Theory.
In: Optimal Control Applications and Methods. (16 May 2021) . - 25 S..
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2732

This is the latest version of this item.

Abstract in another language

This work studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for solving the Hamilton–Jacobi–Bellman partial differential equations specifying CLFs typically require dense state space discretizations and consequently suffer from the curse of dimensionality. A relevant direction of attenuating the curse of dimensionality concerns reducing the computation of the values of CLFs and associated feedbacks at any selected states to finite‐dimensional nonlinear programming problems. We propose to use exit‐time optimal control for that purpose. This article is the first part of a two‐part work. First, we state an exit‐time optimal control problem with respect to a sublevel set of an appropriate local CLF and establish that, under a number of reasonable conditions, the concatenation of the corresponding value function and the local CLF is a global CLF in the whole domain of asymptotic null‐controllability. We also investigate the formulated optimal control problem. A modification of these constructions for the case when one does not find a suitable local CLF is provided as well. Our developments serve as a theoretical basis for a curse‐of‐dimensionality‐free approach to feedback stabilization, that is presented in the second part Yegorov et al. (2021) of this work together with supporting numerical simulation results.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Online First
Keywords: characteristic Cauchy problems; control Lyapunov functions; curse of dimensionality; exit-time optimal control; feedback stabilization; Hamilton–Jacobi–Bellman equations; Pontryagin’s principle
Subject classification: MSC classification: 93D05; 93D15; 49L25
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 28 Apr 2021 09:57
Last Modified: 28 Apr 2021 09:57
URI: https://eref.uni-bayreuth.de/id/eprint/64954

Available Versions of this Item