Pareto Optimality for Linear Mean-Field Delayed Stochastic Systems with $H_{\infty}$ Constraint

This paper is concerned with Pareto optimality under $H_{\infty}$ constraint for linear mean-field delayed stochastic systems disturbed by external disturbances. It is proved that the existence of a Pareto efficient strategy with $H_{\infty}$ constraint is equivalent to finding a relaxed compensator. Furthermore, the resulting Pareto-efficient strategy, presented in an open-loop form, is determined by a stochastic Hamiltonian system. To validate our theoretical findings, a practical example is presented and analyzed by employing the proposed methodology.