American Institute of Mathematical Sciences

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2011, 2011(Special): 1467-1476. doi: 10.3934/proc.2011.2011.1467

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

Sergiy Zhuk 1,

1. 

INRIA Paris-Rocquencourt, Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex, France

Received  July 2010 Revised  August 2010 Published  October 2011

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: Euler- Lagrange equations, Differential-algebraic equations, Descriptor systems, Minimax, State estimation.
Mathematics Subject Classification: Primary: 34K32,49N45x; Secondary: 49N30.
Citation: Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467
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