Examples for separable control Lyapunov functions and their neural network approximation

In this paper, we consider nonlinear control systems and discuss the existence of a separable control Lyapunov function. To this end, we assume that the system can be decomposed into subsystems and formulate conditions such that a weighted sum of Lyapunov functions of the subsystems yields a control Lyapunov function of the overall system. Since deep neural networks are capable of approximating separable functions without suffering from the curse of dimensionality, we can thus identify systems where an efficient approximation of a control Lyapunov function via a deep neural network is possible. A corresponding network architecture and training algorithm are proposed. Further, numerical examples illustrate the behavior of the algorithm. Copyright 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)