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Examples for separable control Lyapunov functions and their neural network approximation

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006761
URN to cite this document: urn:nbn:de:bvb:703-epub-6761-8

Title data

Grüne, Lars ; Sperl, Mario:
Examples for separable control Lyapunov functions and their neural network approximation.
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 approximation 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-6761-8
Date Deposited:	16 Nov 2022 11:09
Last Modified:	16 Nov 2022 11:10
URI:	https://epub.uni-bayreuth.de/id/eprint/6761

Available Versions of this Item

Examples for existence and non-existence of separable control Lyapunov functions. (deposited 27 Sep 2022 07:08)
- Examples for separable control Lyapunov functions and their neural network approximation. (deposited 16 Nov 2022 11:09) [Currently Displayed]

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