RISK-SENSITIVE CONTROL AND DYNAMIC-GAMES FOR PARTIALLY OBSERVED DISCRETE-TIME NONLINEAR-SYSTEMS

In this paper we solve a finite-horizon partially observed risk-sensit ive stochastic optimal control problem for discrete-time nonlinear sys tems and obtain small noise and small risk limits. The small noise lim it is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are o btained. Both the risk-sensitive stochastic control problem and the de terministic dynamic game problem are solved using information states, dynamic programming, and associated separated policies. A certainty eq uivalence principle is also discussed. Our results have implications f or the nonlinear robust stabilization problem. The small risk limit is a standard partially observed risk-neutral stochastic optimal control problem.