Non-Linear Stochastic Control in Continuous State Spaces by Exact Integration in Bellman's Equations

We present an algorithm for sequential control of tasks with non-linear stochastic dynamics in continuous state spaces, characterized by inhomogeneous noise. The algorithm performs approximate value iteration steps on a select set of prototypical states whose cost-to-go is approximated by means of a radial-basis function network. This allows the resulting Bellman's equations to be integrated exactly with respect to the transition densities of a large class of stochastic dynamical systems, resulting in a fast and efficient modified value-iteration procedure.