Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems

Abstract

Solves a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtains 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. The authors' results have implications for the nonlinear robust stabilization problem. The small risk limit is a standard partially observed risk-neutral stochastic optimal control problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>