H 2/H ∞ control problems of backward stochastic systems

Abstract

This paper is concerned with the mixed H 2/H ∞ control problem for a new class of stochastic systems with exogenous disturbance signal. The most distinguishing feature, compared with the existing literatures, is that the systems are described by linear backward stochastic differential equations (BSDEs). The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique. Two equivalent expressions for the H 2/H ∞ control are presented. Contrary to forward deterministic and stochastic cases, the solution to the backward stochastic H 2/H ∞ control is no longer feedback of the current state; rather, it is feedback of the entire history of the state.