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Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. (English) Zbl 1207.93006
Summary: We investigate second-order consensus of multiple nonlinear dynamical mobile agents with a virtual leader in a dynamic proximity network. We assume that only a small fraction of agents in the group have access to the information about the position and velocity of the virtual leader through, for example, certain pre-designed communication mechanism such as wireless broadcasting or sensing. To avoid fragmentation, we propose a connectivity-preserving second-order consensus algorithm. Under the assumption that the initial network is connected, we introduce local adaptation strategies for both the weights on the velocity navigational feedback and the velocity coupling strengths that enable all agents to synchronize with the virtual leader even when only one agent is informed, without requiring any knowledge of the agent dynamics. We finally provide some convincing simulation results to illustrate the theoretical results.
93A14Decentralized systems
93B51Design techniques in systems theory
93C40Adaptive control systems
93C15Control systems governed by ODE
[1]Amir-Moez, R.: Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations, Duke mathematical journal 23, 463-476 (1956) · Zbl 0071.01601 · doi:10.1215/S0012-7094-56-02343-2
[2]Chen, T.; Liu, X.; Lu, W.: Pinning complex networks by a single controller, IEEE transactions on circuits and systems–I: fundamental theory and applications 54, 1317-1326 (2007)
[3]Godsil, C.; Royle, G.: Algebraic graph theory, Graduate texts in mathematics 207 (2001)
[4]Hong, Y.; Gao, L.; Cheng, D.; Hu, J.: Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE transactions on automatic control 52, 943-948 (2007)
[5]Hong, Y.; Hu, J.; Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42, 1177-1182 (2006) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013
[6]Hui, Q.; Haddad, W. M.: Distributed nonlinear control algorithms for network consensus, Automatica 44, 2375-2381 (2008) · Zbl 1153.93307 · doi:10.1016/j.automatica.2008.01.011
[7]Ji, M.; Egerstedt, M.: Distributed coordination control of multiagent systems while preserving connectedness, IEEE transactions on robotics 23, 693-703 (2007)
[8]Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002
[9]Lee, D.; Spong, M. W.: Stable flocking of multiple inertial agents on balanced graphs, IEEE transactions on automatic control 52, 1469-1475 (2007)
[10]Li, X.; Wang, X.; Chen, G.: Pinning a complex dynamical network to its equilibrium, IEEE transactions on circuits and systems–I: fundamental theory and applications 51, 2074-2087 (2004)
[11]Matsumoto, T.: A chaotic attractor from Chua’s circuit, IEEE transactions on circuits and systems 31, 1055-1058 (1984) · Zbl 0551.94020 · doi:10.1109/TCS.1984.1085459
[12]Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control 51, 401-420 (2006)
[13]Peng, K.; Su, H.; Yang, Y.: Coordinated control of multi-agent systems with a varying-velocity leader and input saturation, Communications in theoretical physics 52, 449-456 (2009) · Zbl 1182.93009 · doi:10.1088/0253-6102/52/3/14
[14]Ren, W.: On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control 53, 1053-1059 (2008)
[15]Ren, W.; Atkins, E.: Distributed multi-vehicle coordinated control via local information exchange, International journal of robust and nonlinear control 17, 1002-1033 (2007)
[16]Ren, W.; Beard, R.; Atkins, E.: Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE control systems magazine 27, 71-82 (2007)
[17]Reynolds, C. W. (1987). Flocks, herds, and schools: a distributed behavioral model. In Computer graphics, ACM SIGGRAPH 87 conference proceedings. Vol. 21 (pp. 25–34).
[18]Shi, H.; Wang, L.; Chu, T. G.: Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions, Physica D 213, 51-65 (2006) · Zbl 1131.93354 · doi:10.1016/j.physd.2005.10.012
[19]Shi, H.; Wang, L.; Chu, T. G.: Flocking of multi-agent systems with a dynamic virtual leader, International journal of control 82, 43-58 (2009) · Zbl 1154.93371 · doi:10.1080/00207170801983091
[20]Su, H.; Wang, X.; Chen, G.: Rendezvous of multiple mobile agents with preserved network connectivity, Systems and control letters 59, 313-322 (2010) · Zbl 1191.93005 · doi:10.1016/j.sysconle.2010.03.006
[21]Su, H.; Wang, X.; Chen, G.: A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements, International journal of control 82, 1334-1343 (2009) · Zbl 1168.93311 · doi:10.1080/00207170802549578
[22]Su, H.; Wang, X.; Lin, Z.: Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control 54, 293-307 (2009)
[23]Su, H.; Wang, X.; Lin, Z.: Synchronization of coupled harmonic oscillators in a dynamic proximity network, Automatica 45, 2286-2291 (2009) · Zbl 1179.93102 · doi:10.1016/j.automatica.2009.05.026
[24]Su, H.; Wang, X.; Yang, W.: Flocking in multi-agent systems with multiple virtual leaders, Asian journal of control 10, 238-245 (2008)
[25]Su, H.; Zhang, W.: Second-order consensus of multiple agents with coupling delay, Communications in theoretical physics 51, 101-109 (2009) · Zbl 1172.93305 · doi:10.1088/0253-6102/51/1/20
[26]Vicsek, T.; Cziro’ok, A.; Ben-Jacob, E.; Cohen, O.; Shochet, I.: Novel type of phase transition in a system of self-driven particles, Physical review letters 75, 1226-1229 (1995)
[27]Wang, X.: Complex networks: topology, dynamics, and synchronization, International journal of bifurcation and chaos 12, 885-916 (2002) · Zbl 1044.37561 · doi:10.1142/S0218127402004802
[28]Wang, X.; Chen, G.: Pinning control of scale-free dynamical networks, Physica A 310, 521-531 (2002) · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[29]Wu, C. W.: Synchronization in coupled chaotic circuits and systems, (2002)
[30]Xie, G.; Wang, L.: Consensus control for a class of networks of dynamic agents, International journal of robust and nonlinear control 17, 941-959 (2007)
[31]Yu, W.; Chen, G.; Cao, M.; Kurths, J.: Second-order consensus for multi-agent systems with directed topologies and nonlinear dynamics, IEEE transactions on systems, man and cybernetics, part B (Cybernetics) 40, 881-891 (2010)
[32]Yu, W.; Chen, G.; Lü, J.: On pinning synchronization of complex dynamical networks, Automatica 45, 429-435 (2009) · Zbl 1158.93308 · doi:10.1016/j.automatica.2008.07.016
[33]Zhou, J., Yu, W., Wu, X., Small, M., & Lu, J. (2009). Flocking of multi-agent dynamical systems based on pseudo-leader mechanism. arxiv:0905.1037v1.