Approximate dynamic programming using radial basis functions: A reach-avoid problem

Abstract

We consider finite horizon reach-avoid problems for discrete time stochastic systems with additive Gaussian mixture noise. Our proposed approximation scheme involves relaxing the recursive equations that characterize the optimal value function into inequalities, projecting the optimal value function to a finite dimensional basis and sampling the associated infinite set of constraints. We focus on a specific function parameterization using Gaussian radial basis functions that enables the analytical computation of the one-step reach-avoid reward in the case of hyper-rectangular safe and target sets. We demonstrate the method on a pair of reach-avoid problems involving linear and non-linear dynamics.