Minimax control of discrete nonlinear stochastic systems with noise uncertainty

The author presents a minimax design of linear dynamic compensators for a class of discrete-time nonlinear stochastic systems with uncertain second-order statistical properties. The quadratically optimal linear dynamic compensator for the class of discrete-time nonlinear stochastic systems when the noise covariances are known is derived. It is then assumed that their exact values are unknown but that they belong to known compact sets, and saddle points for this problem are characterized. The time-invariant steady state case is considered where the characterization of saddle points and the relation between the necessary conditions in the optimization problem and the sufficient conditions for controlled systems stability are brought out