On the equivalence between optimal stochastic control and open-loop feedback control

Abstract

The paper is concerned with the question ‘ when is suboptimal open-loop feedback (OLF) control identical to optimal stochastic control ? ’ A lemma about equivalence between the two controls is formulated and used to obtain sufficient conditions for the equivalence in linear quadratic (LQ) problems. It is then shown that the equivalence exists in a generalized class of LQ gaussian (LQG) problems and also in a class of LQ problems having generalized disturbances and complete state information. An introductory section emphasizes the significance of information structure and provides a notation for its discussion in stochastic control problems.