International Journal of Control, Vol.88, No.12, 2554-2562, 2015
H-2/H-infinity control for stochastic systems with delay
This paper is concerned with the H-2/H control problem for stochastic linear systems with delay in state, control and external disturbance-dependent noise. A necessary and sufficient condition for the existence of a unique solution to the control problem is derived. The resulting solution is characterised by a kind of complex generalised forward-backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the equivalent feedback solution via a new type of Riccati equations. To explain the theoretical results, we apply them to a population control problem.
Keywords:stochastic differential equations with delay;H-2;H control;forward-backward stochastic differential equations;Riccati equations