Infinite horizon linear quadratic optimal control for stochastic difference time-delay systems

摘要

The aim of this paper is to investigate the infinite horizon linear quadratic (LQ) optimal control for stochastic time-delay difference systems with both state and control dependent noise. To do this, the notion of exact observability of a stochastic time-delay deference system is introduced and its PBH criterion is presented by the spectrum of an operator related with stochastic time-delay deference systems. Under the assumptions of stabilization and exact observability, it is shown that the optimal control law and optimal value exist, and also the properties of the associated general algebraic Ricatti equation (GARE) are discussed.