Computability of controllers for discrete-time semicontinuous systems

In this paper we consider the computation of controllers for noisy nonlinear discrete-time systems described by upper-semicontinuous multivalued functions. We show that for the problem of controlling to a target set, if an open-loop solution exists, then a feedback controller with can be effectively computed in finite time from the problem data, and that the resulting system is robust with respect to perturbations. We extend the results for systems with partial observations and a dynamic output feedback law based on a finite automaton.