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.

本文研究了弱耦合随机子系统的团队最优控制问题，使用动态规划分解方法识别并利用信息状态获得全局最优策略，控制器观察本地状态和所有子系统平均场状态，信息状态的大小是时间不变的，并且可以推广到无穷时间段的控制设置。该方法针对不同控制器数量且可观测到有噪声的情形有扩展，并以智能电网为例进行了说明。