Title data
Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
Approximation of Separable Control Lyapunov Functions with Neural Networks.
Bayreuth
,
2024
.  11 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007857
This is the latest version of this item.
Project information
Project title: 
Project's official title Project's id Curseofdimensionalityfree nonlinear optimal feedback control with deep neural networks. A compositionalitybased approach via HamiltonJacobiBellman PDEs 463912816 

Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
In this paper, we investigate the ability of neural networks to provide curseofdimensionalityfree 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.
Further data
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Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 11 Nov 2023 22:01)
 Approximation of Separable Control Lyapunov Functions with Neural Networks. (deposited 22 Aug 2024 08:05) [Currently Displayed]