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 Lyapunov function. To end, assume that system can be decomposed into subsystems formulate conditions such weighted sum functions yields function overall system. Since deep neural networks are capable approximating without suffering from curse dimensionality, thus identify where an efficient approximation via network is possible. A corresponding architecture training algorithm proposed. Further, numerical examples illustrate behavior algorithm.