Letters Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics Miaomiao Wang a , Housheng Su a,n , Miaomiao Zhao a , Michael Z.Q. Chen b , Hongwei Wang a a Department of Control Science and Engineering, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Luoyu Road 1037, Wuhan 430074, China b Department of Mechanical Engineering, The University of Hong Kong, Hong Kong article info Article history: Received 8 October 2012 Received in revised form 6 December 2012 Accepted 28 December 2012 Communicated by Long Cheng Available online 4 February 2013 Keywords: Flocking Connectivity-preserving Heterogeneous Nonlinear dynamics Multi-agent system abstract This paper investigates a flocking problem of multiple agents with heterogeneous nonlinear dynamics. In order to avoid fragmentation, we construct a potential function and a connectivity-preserving flocking algorithm to enable the multiple agents to move with the same velocity while preserving the connectivity of underlying networks with a mild assumption that the initial network is connected and the coupling strength of the initial network of the nonlinear velocity consensus term is larger than a threshold value. Furthermore the proposed flocking algorithm is extended to solve the problem of multi-agent systems with a nonlinear dynamical virtual leader. The result is that all agents’ velocities asymptotically approach to the velocity of the virtual leader, and the distance between any two agents is asymptotically stabilized to avoid collisions among agents. Finally, some numerical simulations are presented to illustrate the effectiveness of the theoretical results. & 2013 Elsevier B.V. All rights reserved. 1. Introduction In nature, there exist many interesting collective behaviors such as flocking of birds, schooling of fish, swarming of bacteria and so forth [1]. Flocking is a mechanism in multi-agent systems to achieve velocity synchronization and regulation of relative inter-agent distances with agents obeying some basic rules. For decades, more and more researchers in physics, biology, compu- ter science and control engineering devote themselves to study- ing flocking [2–4]. The application of multi-agent systems can be extended to many fields such as unmanned air vehicles (UAVs) and cooperative control of mobile robots [5–9]. Reynolds developed three heuristic rules in 1987 [2] that led to the appearance of the first computer animation of flocking. The Reynolds rules describe how an individual agent maneuvers itself based on the information of the positions and velocities of its nearby flockmates. A simple flocking model of multiple agents was then proposed by Vicsek et al. [3], where each agent updates its orientation by averaging its own direction and the neighbours’ directions. Recently, Jadbabaie et al. [5] first rigorously proved the convergence of Vicsek’s model. Based on the Vicsek model, Couzin et al. [4] introduced a three-dimensional model of multi-agent with three sensing zones, which can develop into some special phenomena such as torus and highly parallel movement. Olfati-Saber provided a computational and theoretical frame- work in order to design and analyze scalable flocking [10]. In [10], including position and velocity feedback of the virtual leader to every agent in a group, stable flocking motion is achieved under some general initial conditions. In [11], flocking algorithm was investigated in both fixed and switching networks. In [12], the results of [10] are generalized to the situation where only a fraction of agents have information of the leader and the virtual leader has a time-varying velocity. The flocking problem with multiple virtual leaders was studied in [13]. A connectivity- preserving flocking algorithm for multi-agent systems based on position measurements is considered in [14]. Most previous works focus on linear systems especially systems with double-integrator dynamics [5–14]. However, in reality, autonomous agents might be governed by more compli- cated nonlinear dynamics. In fact, in synchronization of complex dynamical networks [15–17], nonlinear dynamics is commonly used. Consensus and flocking of multi-agent systems with some uniform nonlinear dynamics were investigated in [18,19], respec- tively. Using the neural network approximation and the robust control technique, a decentralized consensus algorithm was proposed for multi-agent systems with the uncertain nonlinear dynamics and external disturbances [20]. Furthermore, the authors of [21] extended the novel consensus algorithm in [20] to solve the Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing 0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.neucom.2012.12.033 n Corresponding author. Tel./fax: þ86 27 8754210. E-mail address: houshengsu@gmail.com (H. Su). Neurocomputing 115 (2013) 169–177