Optimal control for a class of noisy linear systems with markovian jumping parameters and quadratic cost

Abstract

Abstract The stochastic optimal control problem is discussed for a class of noisy linear systems with markovian jumping parameters and quadratic cost. First a collection of preliminary results is derived which has an important bearing on the rigorous derivation of the optimal control policy from a dynamic programming standpoint. Then the stochastic control problem for the finite-horizon case is analysed. Finally, a result for the infinite-horizon case (long-run average cost) is presented when the jumping parameter is an irreducible continuous-time Markov chain.