Robust H∞ Consensus Control for High-order Discrete-time Multi-agent Systems With Parameter Uncertainties and External Disturbances
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摘要: 研究了高阶离散多智能体系统的在参数不确定和带外部干扰下的H∞鲁棒一致性控制问题，同时提出线性分布式一致性协议.首先将该问题转化为一组不确定系统的H∞鲁棒控制问题.其次推导出线性矩阵不等式在参数为γ的H∞鲁棒一致性意义下的充分条件.第三，给出了所提出一致性协议在不带外部干扰，参数不确定的高阶离散线性多智能体系统中的收敛效果.最后，通过包含和不包含参数不确定系统的对比仿真实验说明了理论结果的正确性和有效性.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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