Large-scale dynamic system optimization using dual decomposition method with approximate dynamic programming

Abstract

In this paper, multi-agent dynamic optimization with a coupling constraint is studied. The aim is to minimize a strongly convex social cost function, by considering a linear stochastic dynamics for each agent and also coupling constraints among the agents. In order to handle the coupling constraint and also, to avoid high computational cost imposed by a centralized method for large scale systems, the dual decomposition method is used to decompose the problem into multiple individual sub-problems, while the dual variable is adjusted by a coordinator. Nevertheless, since each sub-problem is not a linear–quadratic (LQ) optimal control problem, and hence its closed-form solution does not exist, approximate dynamic programming (ADP) is utilized to solve the sub-problems. The main contribution of the paper is to propose an algorithm by considering the interrelated iterations of dual variable adjustment and ADP, and to prove the convergence of the algorithm to the global optimal solution of the social cost function. Additionally, the implementation of the proposed algorithm using a neural network is presented. Also, the computational advantage of the proposed algorithm in comparison with other bench-marking methods is discussed in simulation results.