Approximation of Separable Control Lyapunov Functions with Neural Networks

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Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
Approximation of Separable Control Lyapunov Functions with Neural Networks.
Bayreuth , 2024 . - 11 S.

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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.