Risk-sensitive control on an infinite time horizon. (English) Zbl 0949.93079

Fleming, Wendell H.; McEneaney, William M.

SIAM J. Control Optimization 33, No. 6, 1881-1915 (1995).

Summary: Stochastic control problems on an infinite time horizon with exponential cost criteria are considered. The Donsker-Varadhan large deviation rate is used as a criterion to be optimized. The optimum rate is characterized as the value of an associated stochastic differential game, with an ergodic (expected average cost per unit time) cost criterion. If we take a small-noise limit, a deterministic differential game with average cost per unit time cost criterion is obtained. This differential game is related to robust control of nonlinear systems.

MSC:

93E20	Optimal stochastic control
93B36	\(H^\infty\)-control
93C10	Nonlinear systems in control theory

Keywords:

risk-sensitive control; \(H^\infty\) control; viscosity solutions; Hamilton-Jacobi equations; Isaacs equations; stochastic control; ergodic cost; infinite time horizon; large deviation; robust control; nonlinear systems