Robust Control of Jump Parameter Systems Governed by Uncertain Chains

We consider an infinite-horizon minimax optimal control problem for nonlinear stochastic uncertain systems governed by a discrete-state continuous-time chain. The chain and system dynamics are subject to uncertain disturbances. Using the large deviations theory we construct a robust stabilizing suboptimal guaranteed-performance controller. Conditions are presented under which this controller is optimal. We then present a numeric algorithm for calculating a robust (sub)optimal controller using a Markov chain approximation technique.