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A class of finite-state and discrete-time optimal control problems isintroduced. The problems involve a large number of agents with independentdynamics, which interact through an aggregative term in the cost function. Theproblems are intractable by dynamic programming. We describe and analyze adecomposition method that only necessitates to solve at each iterationsmall-scale and independent optimal control problems associated with eachsingle agent. When the number of agents is large, the convergence of the methodto a nearly optimal solution is ensured, despite the absence of convexity ofthe problem. The procedure is based on a method called Stochastic Frank-Wolfealgorithm, designed for general nonconvex aggregative optimization problems.Numerical results are presented, for a toy model of the charging management ofa battery fleet.

Decomposed resolution of finite-state aggregative optimal control problems