This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS 1 Fast Consensus Via Predictive Pinning Control Hai-Tao Zhang, Member, IEEE, Michael Z. Q. Chen, Member, IEEE, and Guy-Bart Stan, Member, IEEE Abstract—By incorporating some predictive mechanism into a few pinning nodes, we show that convergence procedure to con- sensus can be substantially accelerated in networks of intercon- nected dynamic agents while physically maintaining the network topology. Such an acceleration stems from the compression mech- anism of the eigenspectrum of the state matrix conferred by the predictive mechanism. This study provides a technical basis for the roles of some predictive mechanisms in widely-spread biolog- ical swarms, flocks, and consensus networks. From the engineering application point of view, inclusion of an efficient predictive mech- anism allows for a significant increase in the convergence speed to- wards consensus. Index Terms—Consensus, multi-agent system (MAS), pinning control, predictive control, synchronization. I. INTRODUCTION O VER the last decade, the collective motion of a group of autonomous agents (or particles) has been a subject of intensive research with potential applications in biology, physics, and engineering. One of the most remarkable charac- teristics of complex dynamical systems such as flocks of birds, schools of fish, or swarms of locusts, is the emergence of a state of collective order in which the agents reach a particular ordered state [1]–[3]. This distributed ordered state seeking problem can be further generalized to a consensus problem [4]–[7], where a group of self-propelled agents agree upon cer- tain quantities of interest such as attitude, position, and so on. Solving consensus problems using distributed computational methods has direct implications on sensor network data fusion, load balancing, swarms/flocks, unmanned air vehicles (UAVs), attitude alignment of satellite clusters, congestion control of communication networks, multi-agent system (MAS) forma- tion control, etc. [8]–[10]. Manuscript received September 04, 2010; revised January 04, 2011; accepted February 07, 2011. The work of H.-T. Zhang was supported in part by the Na- tional Natural Science Foundation of China (NNSFC) under Grant 60704041 and Grant 91023034. The work of G.-B. Stan was supported in part by the EPSRC through the Centre for Synthetic Biology and Innovation at Imperial College London and Program for New Century Excellent Talents in University under Grant 2009343. H.-T. Zhang is with the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China, with the Department of Control Science and Engi- neering, Huazhong University of Science and Technology, Wuhan 430074, China, and also with the Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, U.K.. M. Z. Q. Chen is with the Department of Mechanical Engineering, The Uni- versity of Hong Kong, Hong Kong. G.-B. Stan is with the Department of Bioengineering and Centre for Synthetic Biology and Innovation, Imperial College London, London SW7 2AZ, U.K. and also with the Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, U.K. (e-mail: g.stan@imperial.ac.uk). Digital Object Identifier 10.1109/TCSI.2011.2123450 Convergence rate or speed is an important performance index in the analysis of consensus problems. Among the early works on consensus problems, Tsitsiklis [11] proposed a decentral- ized method to eliminate the disagreement within the group and hence derived the conditions for asymptotic convergence of each agent’s decision sequence. In [4], Olfati-Saber and Murray found the relationship between the eigenvalue distribution of the Laplacian matrix and its consensus performance. By this means, they have established the theoretical foundation of gen- eral consensus problems. To improve the speed of convergence towards consensus, they further proposed a method based on the addition of a few long links to a regular lattice, thus transforming it into a small-world network [12]. In [13], Xiao and Boyd trans- formed the fastest distributed linear averaging problem into a convex optimization problem by considering a particular per- step convergence optimization index, and designed an ultrafast consensus communication-weight assignment method for sym- metric networks. In [14], Jadbabaie et al. derived consensus re- sults for several direction alignment models including the well- known Vicsek model [1]. Specifically, the weak condition re- quiring linkage of the agents on some time intervals is proved to be sufficient for direction consensus. In Ren et al. [5], [6], the strongly connected condition guaranteeing consensus [4] is further relaxed into the existence of a rooted directed spanning tree over time. The most recent research includes the follower representative works: the existence of consensus behavior for a class of MASs was systematically addressed in [15], some nec- essary and sufficient conditions are provided in [16] for second- order consensus in multi-agent dynamic systems, a class of con- strained consensus and optimization problems was studied in [17], a finite-time consensus protocol based on the Lyapunov method was given in [18], a linear quadratic regular (LQR)- based method is proposed in [19] and the outdated information is reused in [20], [21][34] to increase the convergence speed to- wards consensus. In summary, most of the previous works focused on perfor- mance improvements, such as increasing the convergence speed towards consensus, improving the robustness to node and edge failures, or choosing proper interaction graphs possessing suf- ficiently strong algebraic connectivity to guarantee consensus, solely based on the information available at a given time in- stant in the network. It is noted that, in most of the former works, the prediction intelligence of each individual has been ignored. Each agent is only allowed to observe the current be- havior of its neighbors and take a current movement decision based on this instantaneous observation. However, it is well ac- cepted in the biology literature that living creatures typically possess some predictive intelligence allowing them to predict the future movements of their neighbors using their past obser- vations. For example, as early as 1959, Woods [22] designed some bee swarm experiments and provided evidences for the 1549-8328/$26.00 © 2011 IEEE