Minimax state estimation for linear discrete-time differential-algebraic equations

Details Minimax state estimation for linear discrete-time differential-algebraic equations Minimax state estimation for linear discrete-time differential-algebraic equations

2008-07-17

arxiv.org/abs/0807.2769v4

Mathematics

Optimization and Control

to appear in Automatica

Scientific paper

10.1016/j.automatica.2010.06.040

This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements, which belong to a given convex closed bounded set. A new notion of a minimax observable subspace is introduced. By means of the presented approach, new equations describing the dynamics of a minimax recursive estimator for discrete-time non-causal differential-algebraic equations (DAEs) are presented. For the case of regular DAEs it is proved that the estimator's equation coincides with the equation describing the seminal Kalman filter. The properties of the estimator are illustrated by a numerical example.

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