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- W1680595510 abstract "In this report we address the linear state estimation problem: to estimate a linear transformation $ell(varphi)$ of the state $varphi$ through an algorithm $widehat{ell(varphi)}$ operating on measurements $y$, where $Lvarphi=f,y=Hvarphi+eta$. We study the estimation problem in terms of the minimax estimation framework: to find a linear algorithm $widehat{widehat{ell(varphi)}}$ that minimizes the worst case error $sup_{varphi,eta}d(ell(varphi),widehat{ell(varphi)}) $. 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 $mathcal L$ of all solution operators $ell$ 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." @default.
- W1680595510 created "2016-06-24" @default.
- W1680595510 creator A5042402060 @default.
- W1680595510 date "2008-06-27" @default.
- W1680595510 modified "2023-09-27" @default.
- W1680595510 title "Minimax State Estimation for a Dynamic System Described by a Differential-Algebraic Equation" @default.
- W1680595510 hasPublicationYear "2008" @default.
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