Decomposition of convex high dimensional aggregative stochasticcontrol problems

TL;DR

This paper introduces a modified convex high-dimensional stochastic control problem and a decentralized algorithm for its solution, with applications to coordinating large populations of thermostatically controlled loads.

Contribution

It proposes a modified problem that approximates the original and develops a decentralized algorithm with proven convergence, applied to large-scale load coordination.

Findings

The modified problem provides an ε-optimal solution to the original.

The decentralized algorithm converges to the solution of the modified problem.

Application demonstrated in coordinating large populations of TCLs.

Abstract

We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some reasonable assumptions an $\varepsilon$-optimal solution of the original problem. As second contribution, we present a decentralized algorithm whose convergence to the solution of the modified problem is established. Finally, we study the application of the developed tools in an engineering context, studying a coordination problem for large populations of domestic thermostatically controlled loads (TCLs)