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Group Consensus of Heterogenous Continuous-time Multi-agent Systems

Yanxin Zhang

Abstract


This paper considers the group consensus problem for continuous-time linear heterogeneous multi-agent systems with undirected and directed fixed topology. In order to obtain group consensus, we use two partition coefficients to divide all second-order agents and all first-order agents as the two groups, a novel protocol is designed. By constructing the Lyapunov function, a sufficient condition for group consensus under undirected topology are proved. Based on a system transformation method, the group consensus for heterogeneous multi-agent systems is transformed into a group consensus for homogeneous multi-agent systems. We also find the convergence points of the two groups, it has great significance. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.


Keywords


Group consensus; heterogeneous multi-agent systems; undirected topology; directed topology

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References


S. Liu, T. Li, L. Xie, “Continuous-time and sampled-data-based average consensus with logarithmicquantizers”, Automatica, vol. 49, pp. 3329-3336, 2013.

F. Xiao, L. Wang, “Consensus protocols for discrete-time multi-agent systems with time-varying delays”, Automatica, vol. 44, pp. 2577-2582, 2008.

B. Liu, M. Li, J. Zhang, “Synchronization Analysis in Local-interaction Networks with Time-varying Delays”, IEEE International Workshop on Chaos-Fractal Theory and Its Applications, pp. 57-61,2010.

R. Olfati-Saber, “Consensus and cooperation in networked multi-agent systems”, Proc. IEEE, vol.95, pp. 215-233, 2007.

Y. Zheng, L. Wang, “Finite-time consensus of multiple second-order dynamic agents without velocity measurements”, International Journal of Systems Science, vol. 45, no. 3, pp. 579-588, 2014.

A. jadbabaie, J. Lin, A. Morse, “Coordination of group of mobile autonomous agents using nearest neighbor rules”, IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, 2003.

R. O. Saber, R. M. Murray, “Consensus problems in networks of agents with switching topology andtimen-delays, IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, 2004.

W. Yu, G. Chen, M. Cao, “Some necessary and sufficient conditions for second-order consensus inmulti-agent dynamical systems”, Automatica, vol. 46, pp. 1089-1095, 2010.

F. Xiao, L. Wang, “Asynchronous rendezvous analysis via set-valued consensus theory”, SIAM Jour-nal on Control and Optimization, vol. 50, no. 1, pp. 196-221, 2012

Y.Zhang, S.Li, B.Liu, Q.Li, H.S, “Second-order Synchronization of Two Nonlinear Coupled Net-works with Heterogeneous Nonlinear Dynamics and Time-varying Delays”, The 35th Chinese Control Conference, pp. 7891-7896, 2016.

J. N. Tsitsiklis, M. Athans, “Convergence and asymptotic agreement in distributed decision problem-s”, IEEE Transactions on Automatic Control, vol. 29, no. 1, pp. 42-50, 1984.

J. Yu, L. Wang, “Group consensus in multi-agent systems with switching topologies and communication delays”, Syst. Control Lett., vol. 59, no. 6, pp. 340-348, 2010.

J. Yu, M. Yu, J. Hu, B. Liu, “Group consensus in multi-agent systems with sampled data”, The 32thChinese Control Conference, pp. 26-28, 2013.

Y. Feng, S. Xu, B. Zhang, “Group consensus control for double-integrator dynamic multi-agent systems with fixed communication topology”, International Journal of Robust and Nonlinear Control, vol. 24, pp. 532-547, 2014.

Q. Ma, Z. Wang, G. Miao, “Second-order group consensus for multi-agent systems via pinning leader-following approach”, Journal of the Franklin Institute, vol. 351, pp. 1288-1300, 2014.

D. Xie, T. Liang, “Second-order group consensus for multi-agent systems with time delays”, Neuro-computing, vol. 153, pp. 133-139, 2015.

Y. FengX. Tu, J. Li, “Consensus control for a class of heterogeneous multi-Agent systems”, Journal of Computer Applications, vol. 33, no. 6, pp. 1750-1752, 2013.

Y. Sun, G. Zhang, S. Zhang, “Consensus analysis for a class of heterogeneous multi-agent systems infixed and switching topology”, Acta Physica Sinica, vol. 63, no. 22, 2014.

Y. Zheng, L. Wang, “A novel group consensus protocol for heterogeneous multi-agent systems”, International Journal of Control, vol. 88, no. 11, pp. 2347-2353, 2015.

K. Liu, Z. Ji, G. Xie, L. Wang, “Consensus for heterogeneous multi-agent systems under fixed and switching topologies”, Journal of the Franklin Institute, vol. 352, pp. 3670-3683, 2015.

C. Godsil, G. Royal, “Algebraic graph theory”, Springer-Verlag, 2001.

B. Liu, X. Wang, H. Su, Y. Gao, W. Li, “Adaptive Synchronization of Complex Dynamical Networks Governed by Local Lipchitz Nonlinearity on Switching Topology”, Neurocomputing, vol. 118, pp.289-300, 2013.

Y. Zheng, Y. Zhu, L. Wang, “Distributed coordination of heterogeneous multi-agent systems”, 2012.

W. Ren, R.W. Beard, “Distributed consensus in multi-vehicle cooperative control”, Theory and Applications, 2008.

W. Ren, R.W. Beard, “Consensus seeking in multi-agent systems under dynamically changing inter-action topologies”, IEEE Trans. Autom. Control, vol. 50, no. 5, pp. 655-661, 2005.

F. Tan, X. Guan, D. Liu, “Consensus protocol in networked multi-agent systems with non-balanced topology”, Control Theory and Applications, vol. 26, no. 10, pp. 1087-1092, 2009.

A.H. Roger R.J. Charles, “Matrix Analysis”, 1985.




DOI: http://dx.doi.org/10.18686/esta.v4i1.39

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