Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 9Robust H_∞ Control with Variance Constraints: the Finite-Horizon Case

In the real world, there are virtually no strict time-invariant systems since the working circumstances, operating points, or equipment deterioration are of inherently time-varying behaviors. Therefore, the time-varying stochastic systems have started to receive initial yet scattered attention in recent years. Unfortunately, despite the importance of the time-varying nature in system modeling, the covariance control problem for time-varying nonlinear systems has been largely overlooked, not to mention the simultaneous consideration of the H_∞ constraints.

Recognizing the great importance of the time-varying nature of real-time models, this chapter is concerned with the robust H_∞ control problem for a class of uncertain nonlinear discrete time-varying stochastic systems. All the system parameters are time-varying and the uncertainty enters into the state matrix. The nonlinearities under consideration are described by statistical means, which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design a dynamic output feedback controller such that the H_∞ disturbance rejection attenuation level is achieved in the finite horizon while the state covariance is not more than an individual upper bound at each time point. A novel algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that ...