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Volume 2018, Article ID 5950678, 15 pages
Research Article

A Stable Distributed Neural Controller for Physically Coupled Networked Discrete-Time System via Online Reinforcement Learning

Jian Sun1,2 and Jie Li3

1School of Electronic and Information Engineering, Southwest University, Chongqing, China
2Chongqing University Key Laboratory of Networks and Cloud Computing Security, Chongqing, China
3State Grid Chongqing Electric Power Co. Electric Power Research Institute, Chongqing, China

Correspondence should be addressed to Jian Sun; moc.361@nusj_qc

Received 28 July 2017; Revised 21 November 2017; Accepted 21 December 2017; Published 7 February 2018

Academic Editor: Christopher P. Monterola

Copyright © 2018 Jian Sun and Jie Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The large scale, time varying, and diversification of physically coupled networked infrastructures such as power grid and transportation system lead to the complexity of their controller design, implementation, and expansion. For tackling these challenges, we suggest an online distributed reinforcement learning control algorithm with the one-layer neural network for each subsystem or called agents to adapt the variation of the networked infrastructures. Each controller includes a critic network and action network for approximating strategy utility function and desired control law, respectively. For avoiding a large number of trials and improving the stability, the training of action network introduces supervised learning mechanisms into reduction of long-term cost. The stability of the control system with learning algorithm is analyzed; the upper bound of the tracking error and neural network weights are also estimated. The effectiveness of our proposed controller is illustrated in the simulation; the results indicate the stability under communication delay and disturbances as well.