Suboptimal Linear Output Feedback Control of Discrete-Time Systems With Multiplicative Noises

This brief considers the fundamental problem of output feedback control for a class of discrete-time systems with multiplicative noises. It is well-known that the classical separation principle fails due to the existence of multiplicative noises in state and control variables. Thus, the traditional optimal solutions for the controller and estimator can not be obtained. Different from the previous methods of enforced separation principle, the explicit expression of the suboptimal linear controller is derived by using the solution of the forward and backward stochastic difference equations (FBSDEs) and the linear optimal estimator. However, it leads to the other mathematical difficult problem that the control gain and the estimator gain are coupled with each other. Specifically, the control gain obeys the backward Riccati equation and the estimator gain satisfies the forward Riccati equation such that the solutions can not be acquired simultaneously. A novel method of iterative solutions to the coupled backward and forward Riccati equations (CBFREs) is proposed. Numerical examples are illustrated to show that the proposed algorithms have better performance than the previous methods.