Jiang Xiushan, Su Shun-Feng, Zhao Dongya
IEEE Trans Cybern. 2023 Nov;53(11):6963-6976. doi: 10.1109/TCYB.2022.3179605. Epub 2023 Oct 17.
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 H 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 H 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.
本文聚焦于无限时域随机系统的平均场线性二次帕累托（MF-LQP）最优策略设计，该系统在受到外部干扰时具有H约束。基于广义代数黎卡提方程（GARE）的稳定解，首先研究了无限时域中任意初始状态下的随机有界实引理（SBRL）。然后，通过讨论成本泛函的凸性，基于MF-LQ理论和帕累托理论定义并解决了随机不定MF-LQP控制问题。当在协作多智能体系统中考虑最坏情况干扰时，我们表明可以通过求解两个耦合的GARE来给出具有H约束的帕累托最优策略设计[或鲁棒帕累托最优策略，（RPOS）]。当最坏情况干扰和帕累托有效策略起作用时，所有帕累托解都通过一个广义李雅普诺夫方程获得。最后，一个实际例子表明所得到的结果是有效的。
