Value function approximation for the control of multiscale dynamical systems

This paper presents a novel approximate dynamic programming (ADP) algorithm for the optimal control of multiscale dynamical systems comprised of many interacting agents. The ADP algorithm presented in this paper is obtained using a distributed optimal control approach by which the performance of the multiscale dynamical system is represented in terms of a macroscopic state, and is optimized subject to a macroscopic description provided by the continuity equation. A value function approximation scheme is proposed and tested using a data set obtained by solving the necessary conditions for optimality for the distributed optimal control problem. The results shows that the proposed approximation method can learn the value function accurately and, thus, may be applied to adapt the optimal control law.