Abstract
This paper addresses the consensus problem of general linear multi-agent systems with persistent disturbances by distributed output feedback. Suppose that states of agents can not be obtained directly. Several estimators are designed to observe states of agents and the unknown disturbances. A protocol is proposed to drive all agents achieve consensus. Based on the method of model transformation and the property of permutation matrix, sufficient conditions for consensus are obtained in terms of linear matrix inequalities. Finally, simulations are given to show the effectiveness of presented results.
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References
Ren W and Cao Y, Distributed Coordination of Multi-Agent Networks: Emergent Problems, Springer-Verlag, New York, 2010.
Hong Y, Gao L, Chen D, et al., Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE Transactions on Automatic Control, 2007, 52(5): 943–948.
Hu Y, Su H, and James L, Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity, International Journal of Robust and Nonlinear Control, 2013, 23(9): 978–990.
Lin P and Ren W, Constrained consensus in unbalanced networks with communication delays, IEEE Transactins on Automatic Control, 2014, 59(3): 775–781.
Hu J and Zheng W, Adaptive tracking control of leader-follower systems with unknown dynamics and partial measurements, Automatica, 2014, 50(5): 1416–1423.
Wang L, Feng W, Chen Z, et al., Global bounded consensus in heterogeneous multi-agent systems with directed communication graph, IET Control Theory and Applications, 2015, 9(1): 147–152.
Mo L, Niu G, and Pan T, Consensus of heterogeneous multi-agent systems with switching jointlyconnected interconnection, Physica A, 2015, 427: 132–140.
Li Z, Wen W, Liu X, et al., Distributed consensus of linear multi-agent systems with adaptive dynamic protocols, Automatica, 2013, 49(7): 1986–1995.
Li Z, Wen G, Duan Z, et al., Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs, IEEE Transactions on Automatic Control, 2015, 60(4): 1152–1157.
Xu J, Xie L, Li T, et al., Consensus of multi-agent systems with general linear dynamics via dynamic output feedback control, IET Control Theory and Applications, 2013, 7(1): 108–115.
Xi J, He M, Liu H, et al., Admissible output consensualization control for singular multi-agent systems with time delays, Journal of the Franklin Institute, 2016, 353(16): 4074–4090.
Xi J, Fan Z, Liu H, et al., Guaranteed-cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies, Int. J. Robust Nonlinear Control, 2018, 1–12. https://doi.org/10.1002/rnc.4051.
Cai N, Diao C, and Khan MJ, A novel clustering method based on quasi-consensus motions of dynamical multiagent systems, Complexity, 2017, Article ID 4978613, 8 pages.
Zong X, Li T, and Zhang J, Consensus conditions of continuous-time multi-agent systems with additive and multiplicative measurement noises,SIAM Journal on Control and Optimization, 2018, 56(1): 19–52.
Cheng L, Hou Z, and Tan M, A mean-square consensus protocol for linear multi-agent systems with communication noises and fixed topologies, IEEE Transactions on Automatic Control, 2014, 59(1): 261–267.
Cai N, He M, Wu Q, et al., On almost controllability of dynamical complex networks with noises, Journal of Systems Science and Complexity, 2017, DOI: 10.1007/s11424-017-6273-7.
Lin P, Jia Y, and Li L, Distributed robust H∞ consensus control in directed networks of agents with time-delay, Systems and Control Letters, 2008, 57(8): 643–653.
Mo L, Pan T, Guo S, et al., Distributed coordination control of first and second order multi-agent systems with external disturbance, Mathematical Problems in Engineering, 2015, 9: 1–7.
Lin P and Ren W, Distributed H∞ constrained consensus poblem, Systems and Control Letters, 2017, 104: 45–48.
Zhao L, Jia Y, Yu J, et al., H∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances, Applied Mathematics and Computation, 2017, 292: 375–389.
Yucelen T and Egerstedt M, Control of multi-agent systems under persistent disturbances, Proceedings of 2012 American Control Conference, Fairmont Queen Elizabeth, Montreal, Canada, 2012, 5264–5269.
Li Z, Duan Z, and Lewis F, Distributed robust consensus control of multi-agent systems with hererogeneous matching uncertainties, Automatica, 2014, 50(3): 883–889.
Cao W, Zhang J, and Ren W, Leader-follower consensus of linear multi-agent systems with unknown external disturbances, Systems and Control Letters, 2015, 82: 64–70.
Guo S, Mo L, and Pan T, Consensus of linear multi-agent systems with persistent disturbances, Proceedings of 2016 Chinese Intelligent Systems Conference, 2016, 101–110.
Guo S, Mo L, and Yin S, Mean square consensus of multi-agent systems under Markovian switching topologies with colored noises, Journal of Systems Science and Mathematical Sciences, 2017, 37(6): 1427–1438.
Godsil C and Royle G, Algebraic Graph Theory, Springer, New York, 2001.
Kailath T, Linear Systems, Pentice-Hall, New Jersey, 1980.
Li S, Yang J, and Chen W, Generalized extended state observer based control for systems with mismatched uncertainties, IEEE Transactions on Automatic Control, 2012, 59(12): 4792–4802.
Wu W, Chen H, Wang Y, et al., Adaptive exponential stabilization of mobile robots with unknown constant-input disturbance, Journal of Robotic Systems, 2001, 18(6): 289–294.
Li S, Yang J, Chen W, et al., Generalized extended state observer based control for systems with mismatched uncertainties, IEEE Transactions on Industrial Electronics, 2012, 59(12): 4792–4802.
Jia Y, Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: A predictive approach, IEEE Transactions on Automatic Control, 2003, 48(8): 1413–1416.
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This research was supported by the National Natural Science Foundation of China under Grant No. 61304155.
This paper was recommended for publication by Editor LIU Guoping.
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Mo, L., Guo, S. Consensus of Linear Multi-Agent Systems with Persistent Disturbances via Distributed Output Feedback. J Syst Sci Complex 32, 835–845 (2019). https://doi.org/10.1007/s11424-018-7265-y
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DOI: https://doi.org/10.1007/s11424-018-7265-y