Robust H∞ Consensus Control for High-order Discrete-time Multi-agent Systems With Parameter Uncertainties and External Disturbances
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Abstract: The robust H∞ consensus control problem of highorder discrete-time multi-agent systems with parameter uncertainties and external disturbances is studied, and a linear distributed consensus protocol is designed in this paper. Firstly, the robust H∞ consensus control problem of high-order discrete-time multi-agent systems with parameter uncertainties and external disturbances is transformed to a robust H∞ control problem of a set of independent uncertain systems. Secondly, a sufficient linear matrix inequality (LMI) condition is derived to insure that high-order discrete-time multi-agent systems with parameter uncertainties and external disturbances achieve robust consensus with a H∞ performance level γ. Thirdly, convergence results are given as final consensus values of high-order discrete-time linear multi-agent systems with parameter uncertainties and without external disturbances. Finally, a contrast numerical experiment with and without parameter uncertainties is provided to demonstrate the correctness and effectiveness of the theoretical results.
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Key words:
- External disturbances /
- multi-agent systems(MASs) /
- parameter uncertainties /
- robust H∞ consensus control
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[1] A. Sinha and D. Ghose, "Generalization of linear cyclic pursuit with application to rendezvous of multiple autonomous agents, " IEEE Trans. Automat. Control, vol. 51, no. 11, pp. 1819-1824, Nov. 2006. doi: 10.1109/TAC.2006.883033 [2] M. Cao, C. B. Yu, and B. D. O. Anderson, "Formation control using range-only measurements, " Automatica, vol. 47, no. 4, pp. 776-781, Apr. 2011. doi: 10.1016/j.automatica.2011.01.067 [3] R. Olfati-Saber, "Flocking for multi-agent dynamic systems:Algorithms and theory, " IEEE Trans. Automat. Control, vol. 51, no. 3, pp. 401-420, Mar. 2006. doi: 10.1109/TAC.2005.864190 [4] H. T. Zhang, C. Zhai, and Z. Y. Chen, "A general alignment repulsion algorithm for flocking of multi-agent systems, " IEEE Trans. Automat. Control, vol. 56, no. 2, pp. 430-435, Feb. 2011. doi: 10.1109/TAC.2010.2089652 [5] R. Olfati-Saber, "Distributed Kalman filter with embedded consensus filters, " Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 2005, pp. 8179-8184. http://www.academia.edu/1076304/Distributed_Kalman_filter_with_embedded_consensus_filters [6] B. Açskmeşe, M. Mandić, and J. L. Speyer, "Decentralized observers with consensus filters for distributed discrete-time linear systems, " Automatica, vol. 50, no. 4, pp. 1037-1052, Apr. 2014. doi: 10.1016/j.automatica.2014.02.008 [7] M. Barahona and L. M. Pecora, Synchronization in smallworld systems, " Phys. Rev. Lett., vol. 89, no. 5, Article ID:054101, Jul. 2002. doi: 10.1103/PhysRevLett.89.054101 [8] K. Hengster-Movric, K. Y. You, F. L. Lewis, and L. H. Xie, "Synchronization of discrete-time multi-agent systems on graphs using Riccati design, " Automatica, vol. 49, no. 2, pp. 414-423, Feb. 2013. doi: 10.1016/j.automatica.2012.11.038 [9] Z. H. Wang, J. J. Xu, and H. S. Zhang, "Consensusability of multi-agent systems with time-varying communication delay, " Syst. Control Lett., vol. 65, pp. 37-42, Mar. 2014. https://www.researchgate.net/publication/259993252_Consensusability_of_multi-agent_systems_with_time-varying_communication_delay [10] R. O. Saber and R. M. Murray, "Consensus protocols for networks of dynamic agents, " in Proc. 2003 American Control Conference, Denver, CO, USA, 2003, pp. 951-956. [11] R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and timedelays, " IEEE Trans. Automat. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004. doi: 10.1109/TAC.2004.834113 [12] R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multi-agent systems, " Proc. IEEE, vol. 95, no. 1, pp. 215-233, Jan. 2007. doi: 10.1109/JPROC.2006.887293 [13] W. Ren and R. W. Beard, "Consensus seeking in multiagent systems under dynamically changing interaction topologies, " IEEE Trans. Automat. Control, vol. 50, no. 5, pp. 655-661, May 2005. doi: 10.1109/TAC.2005.846556 [14] F. Xiao and L. Wang, "Consensus problems for highdimensional multi-agent systems, " IET Control Theory Appl., vol. 1, no. 3, pp. 830-837, May 2007. doi: 10.1049/iet-cta:20060014 [15] J. X. Xi, N. Cai, and Y. S. Zhong, "Consensus problems for high-order linear time-invariant swarm systems, " Phys. A, vol. 389, no. 24, pp. 5619-5627, Dec. 2010. doi: 10.1016/j.physa.2010.08.038 [16] J. X. Xi, Z. Y. Shi, and Y. S. Zhong, "Consensus and consensualization of high-order swarm systems with time delays and external disturbances, " J. Dyn. Syst. Meas. Control, vol. 134, no. 4, Article ID:041011, May 2012. http://thermalscienceapplication.asmedigitalcollection.asme.org/article.aspx?articleid=1415376 [17] J. X. Xi, Z. Y. Shi, and Y. S. Zhong, "Consensus analysis and design for high-order linear swarm systems with time-varying delays, " Phys. A:Statist. Mech. Appl., vol. 390, no. 23-24, pp. 4114-4123, Nov. 2011. doi: 10.1016/j.physa.2011.06.045 [18] K. Y. You and L. H. Xie, "Network topology and communication data rate for consensusability of discrete-time multiagent systems, " IEEE Trans. Automat. Control, vol. 56, no. 10, pp. 2262-2275, Oct. 2011. doi: 10.1109/TAC.2011.2164017 [19] G. X. Gu, L. Marinovici, and F. L. Lewis, "Consensusability of discrete-time dynamic multiagent systems, " IEEE Trans. Automat. Control, vol. 57, no. 8, pp. 2085-2089, Aug. 2012. doi: 10.1109/TAC.2011.2179431 [20] Y. F. Su and J. Huang, "Two consensus problems for discrete-time multi-agent systems with switching network topology, " Automatica, vol. 48, no. 9, pp. 1988-1997, Sep. 2012. doi: 10.1016/j.automatica.2012.03.029 [21] J. Xu, G. L. Zhang, J. Zeng, J. X. Xi, and B. Y. Du, "Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with parameter uncertainties and timevarying delays, " IET Control Theory Appl., vol. 11, no. 5, pp. 647-667, Mar. 2017. doi: 10.1049/iet-cta.2016.1214 [22] P. Lin, Y. M. Jia, and L. Li, "Distributed robust H∞ consensus control in directed networks of agents with time-delay, " Syst. Control Lett., vol. 57, no. 8, pp. 643-653, Aug. 2008. doi: 10.1016/j.sysconle.2008.01.002 [23] Y. G. Sun and L. Wang, "H∞ consensus of second-order multi-agent systems with asymmetric delays, " Syst. Control Lett., vol. 61, no. 8, pp. 857-862, Aug. 2012. doi: 10.1016/j.sysconle.2012.05.007 [24] Z. K. Li, Z. S. Duan, and G. R. Chen, "On H∞ and H2 performance regions of multi-agent systems, " Automatica, vol. 47, no. 4, pp. 797-803, Apr. 2011. doi: 10.1016/j.automatica.2011.01.054 [25] Y. Liu and Y. M. Jia, "Robust H∞ consensus control of uncertain multi-agent systems with time delays, " Int. J. Control, Automat. Syst., vol. 9, no. 6, pp. 1086-1094, Dec. 2011. doi: 10.1007/s12555-011-0609-1 [26] B. Shen, Z. D. Wang, and X. H. Liu, "Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon, " IEEE Trans. Neural Network, vol. 22, no. 1, pp. 145-157, Jan. 2011. doi: 10.1109/TNN.2010.2090669 [27] Z. D. Wang, D. R. Ding, H. L. Dong, and H. S. Shu, "H∞ consensus control for multi-agent systems with missing measurements:The finite-horizon case, " Syst. Control Lett., vol. 62, no. 10, pp. 827-836, Oct. 2013. doi: 10.1016/j.sysconle.2013.06.004 [28] Q. Y. Liu, Z. D. Wang, X. He, and D. H. Zhou, "Event-Based H∞ consensus control of multi-agent systems with relative output feedback:The finite-horizon case, " IEEE Trans. Automat. Control, vol. 60, no. 9, pp. 2553-2558, Sep. 2015. doi: 10.1109/TAC.2015.2394872 [29] J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations, " IEEE Trans. Automat. Control, vol. 49, no. 9, pp. 1465-1476, Sep. 2004. doi: 10.1109/TAC.2004.834433 [30] Y. Y. Wang, L. H. Xie, and C. E. de Souza, "Robust control of a class of uncertain nonlinear systems, " Syst. Control Lett., vol. 19, no. 2, pp. 139-149, Aug. 1992. doi: 10.1016/0167-6911(92)90097-C [31] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, USA: Society for Industrial and Applied Mathematics, 1994. [32] X. W. Dong, Y. Zhou, Z. Ren, and Y. S. Zhong, "Timevarying formation control for unmanned aerial vehicles with switching interaction topologies, " Control Eng. Pract., vol. 46, pp. 26-36, Jan. 2016. doi: 10.1016/j.conengprac.2015.10.001 [33] X. W. Dong, Y. Zhou, Z. Ren, and Y. S. Zhong, "Timevarying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying, " IEEE Trans. Ind. Electron. , Jul. 2016, doi: 10.1109/TIE.2016.2593656. [34] G. L. Zhang, J. Xu, J. Zeng, J. X. Xi, and W. J. Tang, "Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays, " Trans. Inst. Measur. Control, Feb. 2016, doi: 10.1177/0142331216629197. [35] X. W. Dong, J. X. Xi, Z. Y. Shi, and Y. S. Zhong, "Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances, " Int. J. Syst. Sci. , vol. 44, no. 10, pp. 1843-1856, Oct. 2013. [36] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, USA:Cambridge University Press, 1999. -
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