Distributed Consensus of High-Order Multi-Agents with Nonlinear Dynamics

Author(s)
Jianzhen Li

ABSTRACT

This paper deals with the distributed consensus problem of high-order multi-agent systems with nonlinear dynamics subject to external disturbances. The network topology is assumed to be a fixed undirected graph. Some sufficient conditions are derived, under which the consensus can be achieved with a prescribed norm bound. It is shown that the parameter matrix in the consensus algorithm can be designed by solving two linear matrix inequalities (LMIs). In particular, if the nonzero eigenvalues of the laplacian matrix ac-cording to the network topology are identical, the parameter matrix in the consensus algorithm can be de-signed by solving one LMI. A numerical example is given to illustrate the proposed results.

This paper deals with the distributed consensus problem of high-order multi-agent systems with nonlinear dynamics subject to external disturbances. The network topology is assumed to be a fixed undirected graph. Some sufficient conditions are derived, under which the consensus can be achieved with a prescribed norm bound. It is shown that the parameter matrix in the consensus algorithm can be designed by solving two linear matrix inequalities (LMIs). In particular, if the nonzero eigenvalues of the laplacian matrix ac-cording to the network topology are identical, the parameter matrix in the consensus algorithm can be de-signed by solving one LMI. A numerical example is given to illustrate the proposed results.

Cite this paper

nullJ. Li, "Distributed Consensus of High-Order Multi-Agents with Nonlinear Dynamics,"*Intelligent Control and Automation*, Vol. 2 No. 1, 2011, pp. 1-7. doi: 10.4236/ica.2011.21001.

nullJ. Li, "Distributed Consensus of High-Order Multi-Agents with Nonlinear Dynamics,"

References

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[2] R. Olfati-Saber, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Transactions on Automatic Control, Vol. 51, 2006, pp. 401-420. doi:10.11 09/TAC.2005.864190

[3] H. Su, X. Wang and Z. Lin, “Synchronization of Coupled Harmonic Oscillators in a Dynamic Proximity Network,” Automatica, Vol. 45, 2009, pp. 2286-2291. doi:10.1016/ j.automatica.2009.05.026

[4] J.A. Fax, and R. M. Murray, “Information Flow and Cooperative Control of Vehicle Formations,” IEEE Transactions on Automatic Control, Vol. 49, 2004, pp. 1465-1476. doi:10.1109/TAC.2004.834433

[5] F. Xiao, L. Wang, J. Chen and Y. Gao, “Finite-time formation Control for Multi-Agent Systems,” Automatica, Vol. 45, 2009, pp. 2605-2611. doi:10.1016/j.automatica. 2009.07.012

[6] L. Xiao and S. Boyd, “Fast Linear Iterations for Distributed Averaging,” Systems and Control Letters, Vol. 53, 2004, pp. 65-78. doi:10.1016/j.sysconle.2004.02.022

[7] R. Olfati-Saber and J. S. Shamma, “Consensus Filters for Sensor Networks and Distributed Sensor Fusion,” Proceedings of the IEEE Conference on Decision and Control, 2005, pp. 6698-6703.

[8] R. Olfati-Saber and R. M. Murray, “Consensus Problems in Networks of Agents with Switching Topology and Time-Delays,” IEEE Transactions on Automatic Control, Vol. 49, 2004, pp. 1520-1533. doi:10.1109/TAC.2004. 834113

[9] W. Ren and R. W. Beard, “Consensus Seeking in Multi- agent Systems under Dynamically Changing Interaction Topologies,” IEEE Transactions on Automatic Control, Vol. 50, 2005, pp. 655-661. doi:10.1109/TAC.2005. 846556

[10] W. Ren, “Multi-vehicle Consensus with a Time-Varying Reference State,” Systems Control Letters, Vol. 56, 2007, pp. 474-483. doi:10.1016/j.sysconle.2007.01.002

[11] M. Cao, A. S. Morse and B. O. Anderson, “Agreeing Asynchronously,” IEEE Transactions on Automatic Control, Vol. 53, 2008, pp. 1826-1838. doi:10.1109/TAC. 2008.929387

[12] P. Lin and Y. Jia, “Further Results on Decentralized Coordination in Networks of Agents with Second-Order Dynamics,” IET Control Theory and Applications, Vol. 3, 2009, pp. 957-970. doi:10.1049/iet-cta.2008.0263

[13] W. Yu, G. Chen and M. Cao, “Some Necessary and Sufficient Conditions for Second-Order Consensus in Multi- agent Dynamical Systems,” Automatica, Vol. 46, 2010, pp. 1089-1095. doi:10.1016/j.automatica.2010.03.006

[14] W. Yu, G. Chen, M. Cao and J. Kurths, “Second-Order Consensus for Multi-agent Systems with Directed Topologies and Nonlinear Dynamics,” IEEE Transactions on Systems, Man, and Cybernetics-Part B, Vol. 40, 2010, pp. 881-891. doi:10.1109/TSMCB.2009.2031624

[15] Q. Song, J. Cao and W. Yu, “Second-Order Leader-Following Consensus of Nonlinear Multi-Agent Systems via Pinning Control,” Systems and Control Letters, Vol. 59, 2010, pp. 553-562. doi:10.1016/j.sysconle.2010.06.016

[16] Z. Li, Z. Duan, G. Chen and L. Huang, “Consensus of Multi-Agent Systems and Synchronization of Complex Networks: a Unified Viewpoint,” IEEE Transactions on Circuits and Systems-I, Vol. 57, 2010, pp. 213-224. doi:10.1109/TCSI.2009.2023937

[17] J. H. Seo, H. Shim and J. Back, “Consensus of High- Order Linear Systems using Dynamic Out-Put Feedback Compensator: Low Gain Approach,” Automatica, Vol. 45, 2009, pp. 2659-2664. doi:10.1016/j.automatica.2009.07. 022

[18] P. Lin, Y. Jia and L. Li, “Distributed Robust Consensus Control in Directed Networks of Agents with Time-Delay,” Systems and Control Letters, Vol. 57, 2008, pp. 643-653. doi:10.1016/j.sysconle.2008.01.002

[19] Z. Li, Z. Duan and L. Huang, “ Control of Networked Multi-Agent Systems,” Journal of Systems Science and Complexity, Vol. 22, 2009, pp. 35-48. doi:10.1007/s11424-009-9145-y

[20] Y. Liu and Y. Jia, “Consensus Problems of High-Order Multi-Agent Systems with External Disturbances: An Analysis Approach,” International Journal of Robust and Nonlinear Control, Vol. 20, 2009, pp. 1579- 1593. doi:10.1002/rnc.1531

[21] Y. Liu and Y. Jia, “ Consensus Control of Multi- Agent Systems with Switching Topology: a Dynamic Output Feedback Protocol,” International Journal of Control, Vol. 83, 2010, pp. 527-537. doi:10.1080/0020 7170903267039

[22] G. Young, L. Scardovi and N. Leonard, 2010. “Robustness of Noisy Consensus Dynamics with Directed Communication,” Proceedings of the American Control Conference, 2010, pp. 6312-6317.

[23] S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory,” SIAM Studies in Applied Mathematics. Philadelphia, 1994.

[1] T. Vicsek, A. Czirok, E. Jacob, I. Cohen and O. Schochet, “Novel Type of Phase Transitions in a System of Self- Driven Particles,” Physical Review Letters, Vol. 75, 1995, pp. 1226-1229. doi:10.1103/PhysRevLett.75.1226

[2] R. Olfati-Saber, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Transactions on Automatic Control, Vol. 51, 2006, pp. 401-420. doi:10.11 09/TAC.2005.864190

[3] H. Su, X. Wang and Z. Lin, “Synchronization of Coupled Harmonic Oscillators in a Dynamic Proximity Network,” Automatica, Vol. 45, 2009, pp. 2286-2291. doi:10.1016/ j.automatica.2009.05.026

[4] J.A. Fax, and R. M. Murray, “Information Flow and Cooperative Control of Vehicle Formations,” IEEE Transactions on Automatic Control, Vol. 49, 2004, pp. 1465-1476. doi:10.1109/TAC.2004.834433

[5] F. Xiao, L. Wang, J. Chen and Y. Gao, “Finite-time formation Control for Multi-Agent Systems,” Automatica, Vol. 45, 2009, pp. 2605-2611. doi:10.1016/j.automatica. 2009.07.012

[6] L. Xiao and S. Boyd, “Fast Linear Iterations for Distributed Averaging,” Systems and Control Letters, Vol. 53, 2004, pp. 65-78. doi:10.1016/j.sysconle.2004.02.022

[7] R. Olfati-Saber and J. S. Shamma, “Consensus Filters for Sensor Networks and Distributed Sensor Fusion,” Proceedings of the IEEE Conference on Decision and Control, 2005, pp. 6698-6703.

[8] R. Olfati-Saber and R. M. Murray, “Consensus Problems in Networks of Agents with Switching Topology and Time-Delays,” IEEE Transactions on Automatic Control, Vol. 49, 2004, pp. 1520-1533. doi:10.1109/TAC.2004. 834113

[9] W. Ren and R. W. Beard, “Consensus Seeking in Multi- agent Systems under Dynamically Changing Interaction Topologies,” IEEE Transactions on Automatic Control, Vol. 50, 2005, pp. 655-661. doi:10.1109/TAC.2005. 846556

[10] W. Ren, “Multi-vehicle Consensus with a Time-Varying Reference State,” Systems Control Letters, Vol. 56, 2007, pp. 474-483. doi:10.1016/j.sysconle.2007.01.002

[11] M. Cao, A. S. Morse and B. O. Anderson, “Agreeing Asynchronously,” IEEE Transactions on Automatic Control, Vol. 53, 2008, pp. 1826-1838. doi:10.1109/TAC. 2008.929387

[12] P. Lin and Y. Jia, “Further Results on Decentralized Coordination in Networks of Agents with Second-Order Dynamics,” IET Control Theory and Applications, Vol. 3, 2009, pp. 957-970. doi:10.1049/iet-cta.2008.0263

[13] W. Yu, G. Chen and M. Cao, “Some Necessary and Sufficient Conditions for Second-Order Consensus in Multi- agent Dynamical Systems,” Automatica, Vol. 46, 2010, pp. 1089-1095. doi:10.1016/j.automatica.2010.03.006

[14] W. Yu, G. Chen, M. Cao and J. Kurths, “Second-Order Consensus for Multi-agent Systems with Directed Topologies and Nonlinear Dynamics,” IEEE Transactions on Systems, Man, and Cybernetics-Part B, Vol. 40, 2010, pp. 881-891. doi:10.1109/TSMCB.2009.2031624

[15] Q. Song, J. Cao and W. Yu, “Second-Order Leader-Following Consensus of Nonlinear Multi-Agent Systems via Pinning Control,” Systems and Control Letters, Vol. 59, 2010, pp. 553-562. doi:10.1016/j.sysconle.2010.06.016

[16] Z. Li, Z. Duan, G. Chen and L. Huang, “Consensus of Multi-Agent Systems and Synchronization of Complex Networks: a Unified Viewpoint,” IEEE Transactions on Circuits and Systems-I, Vol. 57, 2010, pp. 213-224. doi:10.1109/TCSI.2009.2023937

[17] J. H. Seo, H. Shim and J. Back, “Consensus of High- Order Linear Systems using Dynamic Out-Put Feedback Compensator: Low Gain Approach,” Automatica, Vol. 45, 2009, pp. 2659-2664. doi:10.1016/j.automatica.2009.07. 022

[18] P. Lin, Y. Jia and L. Li, “Distributed Robust Consensus Control in Directed Networks of Agents with Time-Delay,” Systems and Control Letters, Vol. 57, 2008, pp. 643-653. doi:10.1016/j.sysconle.2008.01.002

[19] Z. Li, Z. Duan and L. Huang, “ Control of Networked Multi-Agent Systems,” Journal of Systems Science and Complexity, Vol. 22, 2009, pp. 35-48. doi:10.1007/s11424-009-9145-y

[20] Y. Liu and Y. Jia, “Consensus Problems of High-Order Multi-Agent Systems with External Disturbances: An Analysis Approach,” International Journal of Robust and Nonlinear Control, Vol. 20, 2009, pp. 1579- 1593. doi:10.1002/rnc.1531

[21] Y. Liu and Y. Jia, “ Consensus Control of Multi- Agent Systems with Switching Topology: a Dynamic Output Feedback Protocol,” International Journal of Control, Vol. 83, 2010, pp. 527-537. doi:10.1080/0020 7170903267039

[22] G. Young, L. Scardovi and N. Leonard, 2010. “Robustness of Noisy Consensus Dynamics with Directed Communication,” Proceedings of the American Control Conference, 2010, pp. 6312-6317.

[23] S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory,” SIAM Studies in Applied Mathematics. Philadelphia, 1994.