STOCHASTIC CONTROL OF IhFINlTE DlMENSIONAL SYSTEMS IN HILBERT SPACE

A factorization perspective to problems of optimal causal estimation and optimal causal control of linear stochastic systems defined on an infinite dimensional Hilbert space is presented. A separation principle is derived when the system input/output map is generated by an abstract evolution operator. The factorization formalism allows for an essentially algebraic approach to these problems.