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URN to cite this document: urn:nbn:de:bvb:703-epub-7857-5
Title data
Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
Approximation of Separable Control Lyapunov Functions with Neural Networks.
Bayreuth
,
2024
. - 11 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 463912816 |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
In this paper, we investigate the ability of 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 network architecture and a training algorithm to illustrate the theoretical findings on a $10$-dimensional control system.
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Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 06 Nov 2023 07:09)
- Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 22 Aug 2024 06:09) [Currently Displayed]
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