In this chapter, it is the aim to solve the robust H∞ filtering problem for a class of time‐varying nonlinear stochastic systems with 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 which is capable of achieving the pre‐specified H∞ performance and meanwhile guaranteeing a minimized upper‐bounded 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 filtering error system is given, guaranteeing 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, hence is suitable for online computation.
Error Variance‐Constrained H∞ Filtering with Degraded Measurements: The Finite‐Horizon Case
2015-03-16
21 pages
Article/Chapter (Book)
Electronic Resource
English