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Approximation of Separable Control Lyapunov Functions with Neural Networks

Title data

Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
Approximation of Separable Control Lyapunov Functions with Neural Networks.
Bayreuth , 2023 . - 12 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007284

Official URL: Volltext

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
463912816

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

In this paper, we investigate the ability of deep neural networks to provide curse-of-dimensionality-free approximations of control Lyapunov functions. To achieve this, we first prove an error bound for the approximation of separable functions with neural networks. Subsequently, we discuss conditions on the existence of separable control Lyapunov functions, drawing upon tools from nonlinear control theory. This enables us to bridge the gap between neural networks and the approximation of control Lyapunov functions as we identify conditions that allow neural networks to effectively mitigate the curse of dimensionality when approximating control Lyapunov functions. Moreover, we present a suitable network architecture and a corresponding training algorithm. The training process is illustrated using two 10-dimensional control systems.

Further data

Item Type: Preprint, postprint
Keywords: control Lyapunov functions; neural networks; curse of dimensionality
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Nov 2023 22:01
Last Modified: 13 Nov 2023 07:51
URI: https://eref.uni-bayreuth.de/id/eprint/87696