Game-Theoretic Design for Robust $H_{\infty}$ Filtering and Deconvolution With Consideration of Known Input

Abstract

This paper aims at the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> estimation of a linear combination of state and unknown input for linear continuous time-varying systems, which is subjected to both norm-bounded parameter uncertainty and a known input. Such a problem is reformulated into a two-player differential game, whose saddle point solution gives rise to both one sufficient solvable condition to the estimation problem and one possible optimal estimator in terms of solution to two coupled Riccati differential equations. It is demonstrated, through one example, the proposed estimator is of superior robust performance with respect to either parameter uncertainty or known input, when compared with those based on the nominal design. Note to Practitioners-Generally speaking, estimation can be divided into two kinds of problems including state observation (filtering, smoothing, and prediction) and deconvolution (unknown input estimation). This paper will consider state and unknown input hybrid estimation (abbreviated to "hybrid estimation"). The estimated signal is linear combination of state and unknown input. Hybrid estimation also reveals useful in many industrial applications. One example is load current estimation of unin terruptible power supply, where load current signal is a linear function of capacity voltage (state) and back electromotive force (unknown input). Chaos synchronization in secure communication is another example. The practical systems are subjected to both norm-bounded parameter uncertainty and a known input, and the known input will incur new estimation error due to parameter uncertainty. In this work, we utilize differential game approach to solve hybrid estimation problem. The method is based on optimal estimator in terms of solution to two coupled Riccati differential equations. Based on these tools, we propose a complete solvable framework for hybrid estimation systems.