On the Existence and Neural Network Representation of Separable Control Lyapunov Functions

Titelangaben

Sperl, Mario ; Mysliwitz, Jonas ; Grüne, Lars:
On the Existence and Neural Network Representation of Separable Control Lyapunov Functions.
Bayreuth , 2025 . - 11 S.

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Abstract

In this paper, we investigate the ability of neural networks to mitigate the curse of dimensionality in representing 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. Moreover, we present a network architecture and a training algorithm to illustrate the theoretical findings on a $10$-dimensional control system.