Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

Abstract

The linear estimation (or optimal control) problem in the emerging area of time-delay systems, multiplicative noise systems, and Markov jump linear systems has been taken into consideration by the control engineers. The purpose of this survey is to provide a review of duality between linear estimation and optimal control in the above-mentioned area. The mentioned subjects are studied to indicate the essential connection between control and estimation problems and to investigate the major cause that the classical duality still holds (not holds) for the broader systems, such as time-delay systems, multiplicative noise systems, Markov jump linear systems, and the like.