Characterization of the optimal disturbance attenuation for nonlinear stochastic partially observable uncertain systems

This paper is concerned with stochastic optimal control systems, in which uncertainty is described by a relative entropy constraint between the nominal measure and the uncertain measure, while the pay-off is a functional of the uncertain measure. This is a minimax game, equivalent to the H/sup /spl infin// optimal disturbance attenuation problem, in which the controller seeks to minimize the pay-off, while the disturbance described by a set of measures aims at maximizing the pay-off. The objective of this paper is to apply the results of the abstract formulation to stochastic uncertain systems, in which the nominal and uncertain systems are described by conditional distributions. The results obtained include existence of the optimal control policy, explicit computation of the worst case conditional measure, and characterization of the optimal disturbance attenuation, for nonlinear partially observable systems. The linear case is presented to illustrate the concepts.