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

Serhiy Zhuk; Serhiy Demidenko; Alexander Nakonechniy

paper

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

arXiv:0704.2212

Abstract

In this paper we study observation problem for linear 2-point BVP Dx=Bf assuming that information about system input f and random noise ηin system state observation model y=Hx+η $i s in co m pl e t e (f an d M η η^{'} a r eso m e a r bi t r a r y e l e m e n t so f g i v e n se t s) . A cr i t er i o n o f g u a r an t ee d (minima x) es t ima t i o n er r or f ini t e n ess i s p r o p ose d . R e p r ese n t a t i o n so f minima x es t ima t i o n s a r eo b t ain e d in t er m so f 2 - p o in tB V P so l u t i o n s . I t i s p r o v e d t ha t in g e n er a l c a se w ec an o n l y es t ima t e a p r o j ec t i o n o f sy s t e m s t a t eo n t oso m e l in e a r mani f o l d$ F $. I n p a r t i c u l a r,$ F=L_2 $i f$ dim N(D H) = 0 $. A l so w e p r o p ose a p r oce d u r e w hi c h d ec i d es i f g i v e n l in e a r f u n c t i o na l b e l o n g s t o$ F$.

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