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Numerical construction of nonsmooth control Lyapunov functions

URN to cite this document: urn:nbn:de:bvb:703-epub-3409-3

Title data

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical construction of nonsmooth control Lyapunov functions.
Bayreuth; Newcastle, Australia , 2017 . - 30 S.

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CLF_MILP_Baier_Braun_Gruene_Kellett_2017.pdf - Preprint
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Project information

Project title:
Project's official titleProject's id
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov FunctionsG1500106

Project financing: ARC (Australian Research Council)

Abstract

Abstract Lyapunov’s second method is one of the most successful tools for analyzing stability properties of dynamical systems. If a control Lyapunov function is known, asymptotic stabilizability of an equilibrium of the corresponding dynamical system can be concluded without the knowledge of an explicit solution of the dynamical system. Whereas necessary and sufficient conditions for the existence of nonsmooth control Lyapunov functions are known by now, constructive methods to generate control Lyapunov functions for given dynamical systems are not known up to the same extent. In this paper we build on previous work to compute (control) Lyapunov functions based on linear programming and mixed integer linear programming. In particular, we propose a mixed integer linear program based on a discretization of the state space where a continuous piecewise affine control Lyapunov function can be recovered from the solution of the optimization problem. Different to previous work, we incorporate a semiconcavity condition into the formulation of the optimization problem. Results of the proposed scheme are illustrated on the example of Artstein’s circles and on a two-dimensional system with two inputs. The underlying optimization problems are solved in Gurobi.

Further data

Item Type: Preprint, postprint
Keywords: control Lyapunov functions; mixed integer programming; dynamical systems
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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 > Advanced Fields > Nonlinear Dynamics
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)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3409-3
Date Deposited: 19 Oct 2017 12:34
Last Modified: 28 Mar 2019 10:19
URI: https://epub.uni-bayreuth.de/id/eprint/3409

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