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Examples for existence and non-existence of separable control Lyapunov functions

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006664
URN to cite this document: urn:nbn:de:bvb:703-epub-6664-9

Title data

Grüne, Lars ; Sperl, Mario:
Examples for existence and non-existence of separable control Lyapunov functions.
Bayreuth , 2022 . - 6 S.

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Project information

Project title:
Project's official title
Project's id
Curse-of-dimensionality-free nonlinear optimal feedback control with deep neural networks. A compositionality-based approach via Hamilton-Jacobi-Bellman PDEs
GR 1569/23-1
Project financing: Deutsche Forschungsgemeinschaft
Deutsche Forschungsgemeinschaft

Abstract

In this paper, we consider nonlinear control systems and discuss the existence of a separable control Lyapunov function. To this end, we assume that the system can be decomposed into subsystems and formulate conditions such that a weighted sum of Lyapunov functions of the subsystems yields a control Lyapunov function of the overall system. Since deep neural networks are capable of approximating separable functions without suffering from the curse of dimensionality, we can thus identify systems where an efficient approximating of a control Lyapunov function via a deep neural network is possible. A corresponding network architecture and training algorithm are proposed. Further, numerical examples illustrate the behavior of the algorithm.

Further data

Item Type: Preprint, postprint
Keywords: deep neural network; curse of dimensionality; separable function; control Lyapunov function; nonlinear control system; small-gain theory
DDC Subjects: 500 Science > 510 Mathematics
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
Research Institutions
Research Institutions > Central research institutes
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-6664-9
Date Deposited: 27 Sep 2022 07:08
Last Modified: 27 Sep 2022 07:09
URI: https://epub.uni-bayreuth.de/id/eprint/6664

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