Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 10Error Variance-Constrained H_∞ Filtering with Degraded Measurements: The Finite-Horizon Case

In this chapter, we aim to solve the robust H_∞ filtering problem for a class of time-varying nonlinear stochastic systems with an error variance constraint. The stochastic nonlinearities considered are quite general, which contain several well-studied stochastic nonlinear systems as special cases. The purpose of the filtering problem is to design a filter that is capable of achieving the pre-specified H_∞ performance and meanwhile guaranteeing a minimized upper bound on the filtering error variance. By means of the adjoint system method, a necessary and sufficient condition for satisfying the H_∞ constraint is first given, expressed as a forward Riccati-like difference equation. Then an upper bound on the variance of the filtering error system is given, guaranteeing that the error variance is not more than a certain value at each sampling instant. The existence condition for the desired filter is established in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time and hence is suitable for online computation. A numerical example is presented finally to show the effectiveness and applicability of the proposed method.

The contributions of this chapter lie in the following parts: (1) For the nonlinear stochastic system, we establish a forward Riccati-like difference equation to solve the H_∞ filtering problem, which can be solved ...