Decomposed resolution of finite-state aggregative optimal control problems

TL;DR

This paper introduces a decomposition method for large-scale finite-state aggregative optimal control problems, enabling efficient solutions despite nonconvexity and large agent numbers, demonstrated through a battery fleet charging example.

Contribution

It proposes a novel decomposition approach using the Stochastic Frank-Wolfe algorithm for nonconvex aggregative control problems with convergence guarantees.

Findings

Method converges to a nearly optimal solution for large agent populations.

Applicable to nonconvex problems without convexity assumptions.

Numerical results validate the approach on a battery fleet charging model.

Abstract

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.