Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters

Pages: 1467 - 1476, Issue Special, September 2011

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Sergiy Zhuk - INRIA Paris-Rocquencourt, Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex, France (email)

Abstract: This paper describes a minimax state estimation approach for linear differential-algebraic equations (DAEs) with uncertain parameters. The approach addresses continuous-time DAEs with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation function. Main result is a Generalized Kalman Duality (GKD) principle, describing a dual control problem. Main consequence of the GKD is an optimal minimax state estimation algorithm for DAEs with non-stationary rectangular matrices. An algorithm is illustrated by a numerical example for 2D timevarying DAE with a singular matrix pencil.

Keywords:  Minimax, State estimation, Differential-algebraic equations, Euler- Lagrange equations, Descriptor systems
Mathematics Subject Classification:  Primary: 34K32,49N45x; Secondary: 49N30

Received: July 2010;      Revised: August 2010;      Published: October 2011.