论文标题
团队对耦合子系统的最佳控制与平均场共享
Team Optimal Control of Coupled Subsystems with Mean-Field Sharing
论文作者
论文摘要
我们研究了团队对随机子系统的最佳控制，这些系统在动力学（通过系统的平均场地）中弱耦合，并任意与成本结合。每个子系统的控制器观察其本地状态和所有子系统状态的平均场。该系统具有非古典信息结构。利用问题的对称性，我们确定信息状态并使用该信息来获得动态编程分解。这个动态程序确定了所有控制器的全球最佳策略。我们的解决方案方法适用于任意数量的控制器，并在噪声观察到平均场时将其推广到设置。信息状态的大小是时间不变的；因此，结果也概括为无限 - 水平控制设置。另外，当观察到没有噪声的平均场时，相应信息状态的大小会随着控制器的数量而多数（而不是指数级）增加，这使我们能够用中等数量的控制器解决问题。我们通过一个由智能网格组成的示例来说明我们的方法，该示例由$ 100 $耦合子系统组成。
We investigate team optimal control of stochastic subsystems that are weakly coupled in dynamics (through the mean-field of the system) and are arbitrary coupled in the cost. The controller of each subsystem observes its local state and the mean-field of the state of all subsystems. The system has a non-classical information structure. Exploiting the symmetry of the problem, we identify an information state and use that to obtain a dynamic programming decomposition. This dynamic program determines a globally optimal strategy for all controllers. Our solution approach works for arbitrary number of controllers and generalizes to the setup when the mean-field is observed with noise. The size of the information state is time-invariant; thus, the results generalize to the infinite-horizon control setups as well. In addition, when the mean-field is observed without noise, the size of the corresponding information state increases polynomially (rather than exponentially) with the number of controllers which allows us to solve problems with moderate number of controllers. We illustrate our approach by an example motivated by smart grids that consists of $100$ coupled subsystems.
