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

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$.