Pareto Optimal Strategy Under H∞ Constraint for the Mean-Field Stochastic Systems in Infinite Horizon
研究了无限时域下受外部干扰的均值场随机系统，在H∞约束下设计帕累托最优策略，通过求解广义代数Riccati方程得到鲁棒帕累托最优解，并用实例验证有效性。
This article focuses on the mean-field linear-quadratic Pareto (MF-LQP) optimal strategy design for stochastic systems in infinite horizon, which is with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> constraint when the system is disturbed by external interferences. The stochastic bounded real lemma (SBRL) with any initial state in infinite horizon is first investigated based on the stabilizing solution of the generalized algebraic Riccati equation (GARE). Then, by discussing the convexity of the cost functional, the stochastic indefinite MF-LQP control problem is defined and solved based on the MF-LQ theory and Pareto theory. When the worst case disturbance is considered in the collaborative multiplayer system, we show that the Pareto optimal strategy design with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> constraint [or robust Pareto optimal strategy, (RPOS)] can be given via solving two coupled GAREs. When the worst case disturbance and the Pareto efficient strategy work, all Pareto solutions are obtained by a generalized Lyapunov equation. Finally, a practical example shows that the obtained results are effective.