Minimax State Estimation for a Dynamic System Described by a Differential-Algebraic Equation
Abstract
In this report we address the linear state estimation problem: to estimate a linear transformation () of the state through an algorithm () operating on measurements y, where L=f,y=H+η. We study the estimation problem in terms of the minimax estimation framework: to find a linear algorithm () that minimizes the worst case error ,ηd((),()) . A key feature of the presented estimation approach is to fix a class of linear operators L, H; given any pair L,H from that class we describe a class L of all solution operators such that the worst case error is finite. We formulate a duality theorem (like Kalman duality principle) that is the estimation problem is equal to the optimal control problem if G is convex bounded subset of the corresponding Hilbert space, L is a closed linear mapping. We obtain optimal estimations as solutions of the linear operator equations if G is an ellipsoid. Then we apply this to the state estimation for the linear differential-algebraic equations (DAE). The minimax observer for DAE is represented in the form of the minimax filter. For discrete time DAEs we present the online minimax estimator.