论文标题
团队最佳解决方案的均值均值耦合LQG子系统
Team-Optimal Solution of Finite Number of Mean-Field Coupled LQG Subsystems
论文作者
论文摘要
考虑了具有线性动力学，二次成本和高斯干扰的分散控制系统。该系统由一个有限数量的子系统组成，其动力学和每步成本函数通过其平均场（经验平均值）耦合。该系统具有平均场共享信息结构，即每个控制器都观察其本地子系统的状态（完美或与噪声）和平均场。结果表明，最佳控制定律在所有子系统中都是独特的，线性的和相同的。此外，通过在完整的观察模型中求解两个解耦的Riccati方程，并在嘈杂的观察模型中求解一个额外的滤波器Riccati方程来计算最佳增益。这些Riccati方程不取决于子系统的数量。还表明，最佳分散性能与最佳集中性能相同。提出了一个由智能网格动机的示例，以说明结果。
A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their mean-field (empirical average). The system has mean-field sharing information structure, i.e., each controller observes the state of its local subsystem (either perfectly or with noise) and the mean-field. It is shown that the optimal control law is unique, linear, and identical across all subsystems. Moreover, the optimal gains are computed by solving two decoupled Riccati equations in the full observation model and by solving an additional filter Riccati equation in the noisy observation model. These Riccati equations do not depend on the number of subsystems. It is also shown that the optimal decentralized performance is the same as the optimal centralized performance. An example, motivated by smart grids, is presented to illustrate the result.
