论文标题
有限状态总体最佳控制问题的分解分解
Decomposed resolution of finite-state aggregative optimal control problems
论文作者
论文摘要
引入了一类有限状态和离散时间最佳控制问题。这些问题涉及大量具有独立动力学的代理，它们通过成本函数中的汇总项相互作用。这些问题通过动态编程而棘手。我们描述和分析了一种分解方法，该方法只需要在每种与每种单一代理相关的小规模和独立的最佳控制问题上解决。当代理的数量很大时，尽管没有问题的凸度，但仍确保该方法与几乎最佳的解决方案的收敛性。该过程基于一种称为随机Frank-Wolfe算法的方法，该算法是为一般非凸聚合优化问题而设计的。为电池舰队充电管理的玩具模型提供了数值结果。
A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an aggregative term in the cost function. The problems are intractable by dynamic programming. We describe and analyze a decomposition method that only necessitates to solve at each iteration small-scale and independent optimal control problems associated with each single agent. When the number of agents is large, the convergence of the method to a nearly optimal solution is ensured, despite the absence of convexity of the problem. The procedure is based on a method called Stochastic Frank-Wolfe algorithm, designed for general nonconvex aggregative optimization problems. Numerical results are presented, for a toy model of the charging management of a battery fleet.
