  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.
