Pareto optimality under H∞ constraint for linear delayed stochastic systems in finite horizon

This paper is concerned with Pareto optimality under $H_{\infty}$ constraint for the indefinite linear quadratic (LQ) cooperative differential game, where the controlled system is described by stochastic delay differential equation (SDDE) and disturbed by external disturbance. By introducing two relaxed compensators, a sufficient condition for Pareto efficient strategy under $H_{\infty}$ constraint is researched, and the resulting Pareto efficient strategy under $H_{\infty}$ constraint in an open-loop form is determined by a stochastic Hamiltonian system. As applications, we use the theoretical results to a production investment problem.