Risk-sensitive optimal control for jump systems with application to sampled-data systems

The optimal stochastic control of jump systems with sampled inputs and observations, which minimizes the expected value of an exponential cost criterion is considered. The information state, which is the sufficient statistics for the problem, is employed to solve the problem. The optimal controller is derived through a combination of the continuous-time and discrete-time Riccati equations. The result for the jump systems is extended to sampled-data systems. Asymptotic behaviors of small noise and small risk limits of the problems, which correspond to deterministic game and risk-neutral stochastic problems, respectively, are also analyzed