Minimax State Observation in Linear One Dimensional 2-Point Boundary Value Problems

Details Minimax State Observation in Linear One Dimensional 2-Point Boundary Value Problems Minimax State Observation in Linear One Dimensional 2-Point Boundary Value Problems

2007-04-17

arxiv.org/abs/0704.2212v1

Mathematics

Optimization and Control

3 pages, 2 figs, to be presented at Int.conf. PDMU-2007 (http://www.unicyb.kiev.ua/ConfPDMU2007)

Scientific paper

In this paper we study observation problem for linear 2-point BVP Dx=Bf assuming that information about system input f and random noise \eta in system state observation model y=Hx+\eta$ is incomplete (f and M\eta\eta' are some arbitrary elements of given sets). A criterion of guaranteed (minimax) estimation error finiteness is proposed. Representations of minimax estimations are obtained in terms of 2-point BVP solutions. It is proved that in general case we can only estimate a projection of system state onto some linear manifold $F$. In particular, $F=L_2$ if $dim N(D H) = 0$. Also we propose a procedure which decides if given linear functional belongs to $F$.

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