Abstract
In this paper, a problem on controllability synthesis for dynamic multi-agent systems with high-order linear protocol is addressed. A particular scenario is considered, in which a given system should be adjusted to be controllable by the input information upon the created leaders, with optional communication links from the leaders to each follower vertex in the graph. It is shown that a single leader is always sufficient to satisfy the requirement for controllability of any given graph topology, so long as there are proper links between the leader and the followers.
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E. G. Gilbert, “Controllability and observability in multivariable control systems,” SIAM J. Control, vol. 1, no. 2, pp. 128–151, 1963.
E. J. Davison and S.-H. Wang, “New results on the controllability and observability of composite systems,” IEEE Trans. Autom. Control, vol. 20, no. 1, pp. 123–128, 1975.
E. J. Davison, “Connectability and structural controllability of composite systems,” Automatica, vol. 13, no. 2, pp. 109–123, 1977.
C.-T. Lin, “Structural controllability,” IEEE Trans. Autom. Control, vol. 19, pp. 201–208, 1974.
R. M. Zazworsky and H. K. Knudsen, “Controllability and observability of linear time-invariant compartmental models,” IEEE Trans. Autom. Control, vol. 23, no. 5, pp. 872–877, 1978.
H. Kobayashi and T. Yoshikawa, “Graph-theoretic approach to controllability and localizability of decentralized control systems,” IEEE Trans. Autom. Control, vol. 27, no. 5, pp. 1096–1108, 1982.
H. G. Tanner, “On the controllability of nearest neighbor interconnections,” Proc. 43rd IEEE Conf. Decision and Control, vol. 3, pp. 2467–2472, 2004.
M. Ji, A. Muhammad, and M. Egerstedt, “Leader-based multi-agent coordination: controllability and optimal control,” Proc. Am. Control Conf., 2006.
A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt, “Controllability of multi-agent systems from a graph-theoretic perspective,” SIAM J. Control Optim., vol. 48, no. 1, pp. 162–186, 2009.
N. Cai and Y.-S. Zhong, “Formation controllability of high order linear time-invariant swarm systems,” IET Control Theory Appl., vol. 4, no. 4, pp. 646–654, 2010.
N. Cai, J.-X. Xi, Y.-S. Zhong, and H.-Y. Ma, “Controllability improvement for linear time-invariant dynamical multi-agent systems,” Int. J. Innov. Comput. I., vol. 8, no. 5a, pp. 3315–3328, 2012.
N. Cai, Swarm Stability and Controllability of High-Order Swarm Systems (In Chinese), Doctoral Dissertation, Tsinghua Univ., Beijing, 2010.
B. Liu, T.-G. Chu, and L. Wang et al., “Controllability of a leader-follower dynamic network with switching topology,” IEEE Trans. Autom. Control, vol. 53, no. 4, pp. 1009–1013, 2008.
L. Wang, F.-C Jiang, G.-M. Xie, and Z. Ji, “Controllability of multi-agent systems based on agreement protocols,” Sci. China Ser. F-Inf. Sci., vol. 52, no. 1, pp. 2074–2088, 2009.
Z.-J. Ji, Z.-D. Wang, H. Lin, and Z. Wang, “Interconnection topologies for multi-agent coordination under leader-follower framework,” Automatica, vol. 45, no. 12, pp. 2857–2863, 2009.
Y. Liu, J. Slotine, and A. Barabasi, “Controllability of complex networks,” Nature, vol. 473, pp. 167–173, 2011.
B. Liu, W.-N. Hu, J. Zhang, and H.-S. Su, “Controllability of discrete-time multi-agent systems with multiple leaders on fixed networks,” Commun. Theor. Phys., vol. 58, no. 6, pp. 856–862, 2012.
W. Ni, X.-L. Wang, and C. Xiong, “Consensus controllability, observability and robust design for leader-following linear multi-agent systems,” Automatica, vol. 49, no. 7, pp. 2199–2205, 2013.
M.-G. Yoon, “Single agent control for cyclic consensus systems,” Int. J. Control Autom. Syst., vol. 11, no. 2, pp. 243–249, 2013.
D.-P. Yang, Z. Chen, and X.-D. Liu, “Distributed adaptive attitude tracking of multiple spacecraft with a leader of nonzero input,” Int. J. Control Autom. Syst., vol. 11, no. 5, pp. 938–946, 2013.
H.-Q. Li, X.-F. Liao, and G. Chen, “Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics,” Int. J. Control Autom. Syst., vol. 11, no. 2, pp. 422–426, 2013.
N. Cai, J.-X. Xi, and Y.-S. Zhong, “Asymptotic swarm stability of high order dynamical multiagent systems: condition and application,” Control and Intelligent Systems, vol. 40, no. 1, pp. 33–39, 2012.
X.-F. Wang, Y. Chen, G. Lu, and Y.-S. Zhong, “Robust flight control of small-scale unmanned helicopter,” Proc. Chinese Control Conf., pp. 2700–2705, 2013.
F. Giulietti, L. Pollini, and M. Innocenti, “Autonomous formation flight,” IEEE Control Syst. Mag., vol. 20, no. 6, pp. 34–44, 2000.
M. G. Richiardi, “Agent-based computational economics: a short introduction,” Knowl. Eng. Rev., vol. 27, no. 2, pp. 137–149, 2012.
J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci., vol. 79, no. 8, pp. 2554–2558, 1982.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
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Recommended by Associate Editor Shengyuan Xu under the direction of Editor Zengqi Sun.
This work was supported by National Natural Science Foundation of China (Grants 61263002, 61374054, 61174067 & 614722 00), and by Program for Young Talents of SEAC China (Grant [2013] 231).
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Cai, N., Cao, J. & Junaid Khan, M. A controllability synthesis problem for dynamic multi-agent systems with linear high-order protocol. Int. J. Control Autom. Syst. 12, 1366–1371 (2014). https://doi.org/10.1007/s12555-013-0374-4
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DOI: https://doi.org/10.1007/s12555-013-0374-4