O'Reilly logo

Variance-Constrained Multi-Objective Stochastic Control and Filtering by Yuming Bo, Zidong Wang, Lifeng Ma

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required