Pareto optimal strategy for linear stochastic systems with H∞ constraint in finite horizon

Abstract

In this paper, we derive conditions for the existence of Pareto efficient strategy and Pareto solution under H∞ constraint for the linear quadratic (LQ) finite horizon cooperative differential game of stochastic systems with state-, control- and disturbance-multiplicative noise. Firstly, we present a stochastic bounded real lemma (SBRL) with any initial condition for the considered stochastic system. Next, a necessary and sufficient condition for Pareto optimal strategy under the H∞ constraint is researched by two cross-coupled generalized differential Riccati equations (GDREs), which is the key contribution of this paper. Another contribution is that the Pareto solution for every controller is given under the Pareto efficient strategy and worst-case external disturbance. Finally, a practical example is given to illustrate the effectiveness of our results.