Risk-Sensitive Control and Dynamic Games for Partially Observed Discrete - Time Nonlinear Systems
James, Matthew R.
Baras, John S.
Elliott, Robert J.
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In this paper we solve a finite-horizon partially observed risk- sensitive stochastic optimal control problem for discrete-time nonlinear systems, and obtain small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states, dynamic programming, and associated separated policies. A certainty equivalence principle is also discussed. Our results have implications for the nonlinear robust stabilization problem. The small risk limits is a standard partially observed risk neutral stochastic optimal control problem.