Approximate viability using quasi-random samples and a neural network classifier

Abstract

We propose a novel approach to the computational investigation of reachability properties for nonlinear control systems. Our goal is to combat the curse of dimensionality, by proposing a mesh-free algorithm to numerically approximate the viability kernel of a given compact set. Our algorithm is based on a non-smooth analysis characterization of the viability kernel. At its heart is a neural network classifier based on Bayesian regularization, which operates on a pseudorandom sample extracted from the state-space (instead of a regular grid). The algorithm was implemented in Matlab and applied successfully to examples with linear and nonlinear dynamics.