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

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  • 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.
    Mathematics Subject Classification: Primary: 34K32,49N45x; Secondary: 49N30.


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