This paper studies optimal linear quadratic regulation (LQR) problem of discrete-time interconnected systems (ISs) defined over a weakly connected graph. Subsystems in an IS share information based on the topology of the system. The main challenge of this work in comparison to the standard LQR problem, stems from that a subsystem may never acquire information from some other subsystems, due to the weakly connected topology. In this paper, a multiple-step estimation approach is proposed to analytically design the optimal controller for ISs with weakly connected topology. Also, the optimal value of the cost function is explicitly derived. Finally, the effectiveness of the proposed method is illustrated by simulations using a connected vehicle system.

本文研究了在弱连通图上定义的离散时间互连系统 (IS) 的最优线性二次调节 (LQR) 问题。IS 中的子系统基于系统的拓扑共享信息。与标准 LQR 问题相比，这项工作的主要挑战在于，由于弱连接拓扑，一个子系统可能永远不会从其他一些子系统获取信息。在本文中，提出了一种多步估计方法来分析设计具有弱连接拓扑的 IS 的最优控制器。此外，成本函数的最优值是明确导出的。最后，通过使用连接的车辆系统进行的仿真说明了所提出方法的有效性。