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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.

MSC:

93A14 Decentralized systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93C40 Adaptive control/observation systems
93C15 Control/observation systems governed by ordinary differential equations

Software:

Boids
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[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
[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) · Zbl 1374.93297
[3] Godsil, C.; Royle, G., (Algebraic graph theory. Algebraic graph theory, Graduate texts in mathematics, Vol. 207 (2001), Springer: Springer New York) · Zbl 0968.05002
[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) · Zbl 1366.93437
[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
[6] Hui, Q.; Haddad, W. M., Distributed nonlinear control algorithms for network consensus, Automatica, 44, 2375-2381 (2008) · Zbl 1153.93307
[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), Prentice Hall: Prentice Hall Upper Saddle River, NJ · Zbl 0626.34052
[9] Lee, D.; Spong, M. W., Stable flocking of multiple inertial agents on balanced graphs, IEEE Transactions on Automatic Control, 52, 1469-1475 (2007) · Zbl 1366.93503
[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) · Zbl 1374.94915
[11] Matsumoto, T., A chaotic attractor from Chua’s circuit, IEEE Transactions on Circuits and Systems, 31, 1055-1058 (1984) · Zbl 0551.94020
[12] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Transactions on Automatic Control, 51, 401-420 (2006) · Zbl 1366.93391
[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
[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) · Zbl 1266.93010
[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)
[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
[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
[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
[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
[22] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE Transactions on Automatic Control, 54, 293-307 (2009) · Zbl 1367.37059
[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
[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
[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
[28] Wang, X.; Chen, G., Pinning control of scale-free dynamical networks, Physica A, 310, 521-531 (2002) · Zbl 0995.90008
[29] Wu, C. W., Synchronization in coupled chaotic circuits and systems (2002), World Scientific: World Scientific Singapore · Zbl 1007.34044
[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) · Zbl 1266.93013
[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
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