Abstract
This paper considers the distributed tracking control of uncertain nonlinear multi-agent systems in the presence of unmeasured states and unknown input of the leader over an undirected network. By approximating the uncertain nonlinear dynamics via neural network and constructing a local observer to estimate the unmeasured states, distributed output feedback tracking controllers, with static and dynamic coupling gains, respectively, are proposed, based on the relative observed states of neighboring agents. It is proved that with the developed controllers, the state of each agent synchronizes to that of the leader for any undirected connected graphs even when only a fraction of the agents in the network have access to the state information of the leader, and the distributed tracking errors are uniformly ultimately bounded. A sufficient condition to the existence of the distributed controllers is that each agent is stabilizable and detectable. Future works include an extension to the directed network topologies.
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References
Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Automa. Control 49(9), 1465–1476 (2004)
Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automa. Control 48(6), 988–1001 (2003)
Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-Agent systems. Proc. IEEE 95(1), 215–233 (2007)
Ren, W., Beard, R., Atkins, E.: Information consensus in multivehicle cooperative control. IEEE Control Syst. Mag. 27(2), 71–82 (2007)
Ren, W., Beard, R.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Automa. Control 50(5), 655–661 (2005)
Hong, Y.G., Hu, J.P., Gao, L.X.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7), 1177–1182 (2006)
Ren, W.: Multi-vehicle consensus with a time-varying reference state. Syst. & Control Lett. 56(7), 474–483 (2007)
Wang, X.L., Hong, Y.G., Huang, J., Jiang, Z.P.: A distributed control approach to a robust output regulation problem for multi-agent linear systems. IEEE Trans. Automa. Control 55(12), 2891–2895 (2010)
Hong, Y.G., Wang, X.L., Jiang, Z.P.: Distributed output regulation of leader-follower multi-agent systems. Int. J. Robust Nonlin. 23(1), 48–66 (2013)
Li, Z.K., Duan, Z.S., Chen, G.R., Huang, L.: Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Trans. Circuits Syst. I, Reg. Papers 57(1), 213–224 (2010)
Li, Z.K., Liu, X.D., Ren, W., Xie, L.H.: Distributed tracking control for linear multi-Agent systems with a leader of bounded unknown input. IEEE Trans. Automa. Control 58(2), 518–523 (2013)
Ni, W., Cheng, D.Z.: Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst. & Control Lett. 59(4), 209–217 (2010)
Zhang, H.W., Lewis, F.L., Das, A.: Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Automa. Control 56(8), 1948–1952 (2011)
Hou, Z.G., Cheng, L., Tan, M.: Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst., Man, Cybern. Part B: Cybern. 39(3), 636–647 (2009)
Das, A., Lewis, F.L.: Distributed adaptive control for synchcronization of unknown nonlinear networked systems. Automatica 26(12), 2014–2021 (2010)
Das, A., Lewis, F.L.: Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. Int. J. Robust Nonlin. 21(13), 1509–1524 (2011)
Cheng, L., Hou, Z.G., Tan, M., Lin, Y.Z., Zhang, W.J.: Neural-network-based adaptive leader-following control for multiagent systems with uncertainties. IEEE Trans. Neural Netw. Learn. Syst. 21(8), 1351–1358 (2010)
Hu, G.Q.: Robust consensus tracking of a class of second-order multi-agent dynamic systems. Syst. & Control Lett. 61(1), 134–142 (2012)
Zhang, H.W., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(7), 1432–1439 (2012)
Cui, R.X., Ren, B.B., Ge, S.S.: Synchronised tracking control of multi-agent system with high-order multi-agent systems. IET Control Theory Appl. 6(5), 603–614 (2012)
Zhang, H.W., Lewis, F.L., Qu, Z.H.: Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Trans. Ind. Electron. 59(7), 3026–3041 (2012)
Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 6(1), 195–202 (2005)
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Peng, Z., Wang, D., Zhang, H. (2013). Distributed Output Feedback Tracking Control of Uncertain Nonlinear Multi-Agent Systems with Unknown Input of Leader. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39068-5_2
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DOI: https://doi.org/10.1007/978-3-642-39068-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39067-8
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