Please cite this article in press as: J. Ebegbulem, M. Guay, Distributed control of multi-agent systems over unknown communication networks using extremum seeking, J. Process Control (2017), http://dx.doi.org/10.1016/j.jprocont.2017.09.002 ARTICLE IN PRESS G Model JJPC-2205; No. of Pages 12 Journal of Process Control xxx (2017) xxx–xxx Contents lists available at ScienceDirect Journal of Process Control j ourna l ho me pa ge: www.elsevier.com/locate/jprocont Distributed control of multi-agent systems over unknown communication networks using extremum seeking Judith Ebegbulem, Martin Guay * Department of Chemical Engineering, Queen’s University, Kingston, ON, Canada a r t i c l e i n f o Article history: Received 31 May 2016 Received in revised form 29 August 2017 Accepted 2 September 2017 Available online xxx Keywords: Distributed control Extremum seeking control Consensus estimation Unknown communication networks Real-time optimization Multi-agent systems a b s t r a c t In this paper, the solution of large-scale real-time optimization problems of multi-agent systems (MAS) is tackled in a distributed and a cooperative manner without the requirement of exact knowledge of network connectivity. Each agent in the communication network measures a local disagreement cost in addition to its local cost. The agents must work collaboratively to ensure that the system’s unknown overall cost (i.e., the sum of the local cost of all the agents) is minimized. In order to minimize this cost, the local disagreement cost of all the agents must first be minimized. This minimization requires the solution of a consensus estimation problem and ensures that the agents reach agreement on their decision variables. To address this challenging problem, a distributed proportional-integral extremum seeking control technique is proposed, one that solves both problems simultaneously. Three simulation examples are included, they demonstrate the effectiveness and robustness of the proposed technique. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Several control techniques have been proposed and employed in solving real-time optimization problems, they range from model based to model free. When the situation entails addressing large- scale real-time optimization problems involving multi-agents, these techniques are basically grouped as either centralized or distributed (decentralized). In a centralized environment, a single decision maker controls the actions of all agents in the system. This decision maker monitors, receives and processes information from and sends processed results back to the agents. This means that the decision maker has complete knowledge of the state of the system at all times and can make useful decision(s) that help meet global objective(s). One draw back of this approach is the increase in com- putational complexity that arises as the number of agents increases. This could result in the transmission of inaccurate information, loss of information and increase in computation time. In addition, centralized approaches are complex, expensive and problem spe- cific. Furthermore, centralized approaches lack system robustness as they are inefficient in a dynamic environment and the failure of the decision maker could mean failure of the entire system. * Corresponding author. E-mail addresses: 13je11@queensu.ca (J. Ebegbulem), guaym@queensu.ca (M. Guay). Most of the challenges highlighted above are absent in a dis- tributed environment. This is because a distributed approach involves multiple decision makers that are able to make individ- ual decisions. Each decision maker controls an agent and limits the agent’s task to the solution of a simpler local problem. Each local problem can be tackled in a cooperative (through local communica- tion with neighbouring agents) or an uncooperative fashion. Some of the advantages of distributed control over centralized control include but are not limited to effectiveness, flexibility, scalability and adaptiveness. The greatest advantage of distributed control is system robustness. This implies that the failure of a decision maker does not necessarily mean overall system failure as the system can absorb the effect of a failure and quickly recover through the help of other decision makers. In light of the advantages of distributed control, extensive research is being carried out in addressing control and optimization problems of MAS in a cooperative and an uncooperative manner. Researchers are focused on the development and analysis of new distributed techniques for the solution of such problems which are obviously difficult or impossible to solve using centralized approaches. Solving distributed control problems may require the agents in the network to reach agreement on some quantity of interest. This means solving a consensus estimation problem and such problems can be tackled using a consensus estimator. Sev- eral consensus algorithms have been proposed in the literature, see [1–6]. Distributed techniques have been proposed to tackle resource allocation problems. In a distributed but an uncoopera- http://dx.doi.org/10.1016/j.jprocont.2017.09.002 0959-1524/© 2017 Elsevier Ltd. All rights reserved.