Shi, Hong; Wang, Long; Chu, Tianguang Flocking of multi-agent systems with a dynamic virtual leader. (English) Zbl 1154.93371 Int. J. Control 82, No. 1, 43-58 (2009). Summary: This paper considers the flocking problem of a group of autonomous agents moving in Euclidean space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighbouring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighbouring agents and the external reference signal (or ‘virtual leader’). Then we prove that, if the acceleration of the virtual leader is known, then each agent can follow the virtual leader, and the convergence rate of the centre of mass (CoM) can be estimated; if the acceleration is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, thus the flocking motion can be obtained. However, in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to illustrate our theoretical results. Cited in 21 Documents MSC: 93C15 Control/observation systems governed by ordinary differential equations 93C85 Automated systems (robots, etc.) in control theory Keywords:collective dynamic behaviour; flocking; multiagent systems; swarm intelligence; virtual leader Software:Boids PDFBibTeX XMLCite \textit{H. Shi} et al., Int. J. Control 82, No. 1, 43--58 (2009; Zbl 1154.93371) Full Text: DOI References: [1] DOI: 10.1016/j.chaos.2005.08.133 · Zbl 1142.34346 · doi:10.1016/j.chaos.2005.08.133 [2] Clarke FH, Optimization and Nonsmooth Analysis (1983) [3] DOI: 10.1109/TAC.2004.834433 · Zbl 1365.90056 · doi:10.1109/TAC.2004.834433 [4] DOI: 10.1109/TAC.2003.809765 · Zbl 1365.92143 · doi:10.1109/TAC.2003.809765 [5] Godsil C, Algebraic Graph Theory (2001) [6] DOI: 10.1016/j.automatica.2006.02.013 · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013 [7] Horn RA, Matrix Analysis (1985) [8] DOI: 10.1109/TAC.2003.812781 · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781 [9] Leonard, NE and Fiorelli, E. 2001. Virtual Leaders, Artificial Potentials and Coordinated Control of Groups. Proceedings of the 40th IEEE Conf. Decision and Control, 3. 2001. pp.2968–2973. [10] DOI: 10.1109/TAC.2004.825639 · Zbl 1365.93208 · doi:10.1109/TAC.2004.825639 [11] DOI: 10.1109/TAC.2004.834113 · Zbl 1365.93301 · doi:10.1109/TAC.2004.834113 [12] DOI: 10.1109/TAC.2005.864190 · Zbl 1366.93391 · doi:10.1109/TAC.2005.864190 [13] DOI: 10.1109/TCS.1987.1086038 · Zbl 0632.34005 · doi:10.1109/TCS.1987.1086038 [14] Reynolds, CW. 1987. Flocks, Herds, and Schools: A Distributed Behavioral Model. ACM SIGGRAPH ’87 Conference Proceedings, Computer Graphics, 21. 1987. pp.25–34. [15] DOI: 10.1109/TAC.2004.829621 · Zbl 1365.93327 · doi:10.1109/TAC.2004.829621 [16] DOI: 10.1109/9.317122 · Zbl 0814.93049 · doi:10.1109/9.317122 [17] Shi H, in Lecture Notes in Artificial Intelligence 3630 pp 604– (2005) [18] Shi, H, Wang, L, Chu, T and Xiao, F. Self-organization of General Multi-agent Systems with Complex Interactions. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. 2006, Beijing, China. pp.3203–3208. [19] DOI: 10.1016/j.physd.2005.10.012 · Zbl 1131.93354 · doi:10.1016/j.physd.2005.10.012 [20] DOI: 10.1109/TAC.2007.895948 · Zbl 1366.93414 · doi:10.1109/TAC.2007.895948 [21] Tanner, HG, Jadbabaie, A and Pappas, GJ. Stable Flocking of Mobile Agents, Part I: Fixed Topology; Part II: Dynamic Topology. Proceedings of the 42nd IEEE Conference of Decision and Control, 2. 2003. pp.2010–2015. 2016–2021 [22] DOI: 10.1103/PhysRevLett.75.1226 · doi:10.1103/PhysRevLett.75.1226 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.