Speaker
Description
In this talk, we explore the representation of control Lyapunov functions using neural networks. First, we demonstrate that, under suitable assumptions regarding the decomposition of a given control system into subsystems, a smooth control Lyapunov function with a separable structure exists. This separable structure enables its representation via neural networks requiring a number of neurons that increases only polynomially with the state dimension, thereby avoiding the curse of dimensionality. Next, we address the practically relevant scenario where a smooth control Lyapunov function does not exist. We establish conditions under which nonsmooth control Lyapunov functions exist that can be represented using neural networks with a suitable number of ReLU layers. These theoretical results are supported by illustrative numerical test cases.
