SCIENCE CHINA Information Sciences, Volume 60, Issue 7: 070202(2017) https://doi.org/10.1007/s11432-016-9125-2

Formation control with disturbance rejection for a class of Lipschitz nonlinear systems

More info
  • ReceivedApr 26, 2017
  • AcceptedJun 8, 2017
  • PublishedJun 13, 2017


In this paper, we consider the leader-follower formation control problem for general multi-agent systems with Lipschitz nonlinearity and unknown disturbances. To deal with the disturbances, a disturbance observer-based control strategy is developed for each follower. Then, a time-varying formation protocol is proposed based on the relative state of the neighbouring agents and sufficient conditions for global stability of the formation control are identified using Lyapunov method in the time domain. The proposed strategy and analysis guarantee that all signals in the closed-loop dynamics are uniformly ultimately bounded and the formation tracking errors converge to an arbitrarily small residual set. Finally, the validity of the proposed controller is demonstrated through a numerical example.


This work was supported by National Natural Science Foundation of China (Grant No. 61673034) and China Scholarship Council (CSC).


[1] Ren W, Beard R W. Distributed Consensus in Multi-Vehicle Cooperative Control. London: Springer-Verlag, 2008. Google Scholar

[2] Jadbabaie A, Jie Lin A, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr, 2003, 48: 988-1001 CrossRef Google Scholar

[3] Olfati-Saber R, Murray R M. Consensus Problems in Networks of Agents With Switching Topology and Time-Delays. IEEE Trans Automat Contr, 2004, 49: 1520-1533 CrossRef Google Scholar

[4] Wei Ren , Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr, 2005, 50: 655-661 CrossRef Google Scholar

[5] Li Z K, Duan Z S, Chen G R, et al. Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans Circuits Syst I, 2010, 57: 213--224. Google Scholar

[6] Yu W, Chen G, Lü J. Synchronization via Pinning Control on General Complex Networks. SIAM J Control Optim, 2013, 51: 1395-1416 CrossRef Google Scholar

[7] Li Z, Ren W, Liu X. Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols. IEEE Trans Automat Contr, 2013, 58: 1786-1791 CrossRef Google Scholar

[8] Keyou You , Lihua Xie . Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems. IEEE Trans Automat Contr, 2011, 56: 2262-2275 CrossRef Google Scholar

[9] Wang C, Zuo Z, Lin Z. A Truncated Prediction Approach to Consensus Control of Lipschitz Nonlinear Multi-Agent Systems with Input Delay. IEEE Trans Control Netw Syst, 2016, : 1-1 CrossRef Google Scholar

[10] Liu S, Xie L, Lewis F L. Synchronization of multi-agent systems with delayed control input information from neighbors. Automatica, 2011, 47: 2152-2164 CrossRef Google Scholar

[11] Zuo Z. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 2015, 54: 305-309 CrossRef Google Scholar

[12] Qiu Z, Liu S, Xie L. Distributed constrained optimal consensus of multi-agent systems. Automatica, 2016, 68: 209-215 CrossRef Google Scholar

[13] Li T, Fu M, Xie L. Distributed Consensus With Limited Communication Data Rate. IEEE Trans Automat Contr, 2011, 56: 279-292 CrossRef Google Scholar

[14] Ding Z, Li Z. Distributed adaptive consensus control of nonlinear output-feedback systems on directed graphs. Automatica, 2016, 72: 46-52 CrossRef Google Scholar

[15] Consolini L, Morbidi F, Prattichizzo D. Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica, 2008, 44: 1343-1349 CrossRef Google Scholar

[16] Duan H B, Luo Q N, Yu Y X. Trophallaxis network control approach to formation flight of multiple unmanned aerial vehicles. Sci China Tech Sci, 2013, 56: 1066--1074. Google Scholar

[17] Balch T, Arkin R C. Behavior-based formation control for multirobot teams. IEEE Trans Robot Automat, 1998, 14: 926-939 CrossRef Google Scholar

[18] Oh K K, Park M C, Ahn H S. A survey of multi-agent formation control. Automatica, 2015, 53: 424-440 CrossRef Google Scholar

[19] Fax J A, Murray R M. Information Flow and Cooperative Control of Vehicle Formations. IEEE Trans Automat Contr, 2004, 49: 1465-1476 CrossRef Google Scholar

[20] Ren W. Consensus strategies for cooperative control of vehicle formations. IET Control Theor Appl, 2007, 1: 505-512 CrossRef Google Scholar

[21] Ren W, Sorensen N. Distributed coordination architecture for multi-robot formation control. Robotics Autonomous Syst, 2008, 56: 324-333 CrossRef Google Scholar

[22] Dong X, Xi J, Lu G. Formation Control for High-Order Linear Time-Invariant Multiagent Systems With Time Delays. IEEE Trans Control Netw Syst, 2014, 1: 232-240 CrossRef Google Scholar

[23] Qu Z H. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. London: Springer-Verlag, 2009. Google Scholar

[24] Zhang X Y, Duan H B, Yu Y X. Receding horizon control for multi-UAVs close formation control based on differential evolution. Sci China Inf Sci, 2010, 53: 223--235. Google Scholar

[25] Sun C, Duan H, Shi Y. Optimal Satellite Formation Reconfiguration Based on Closed-Loop Brain Storm Optimization. IEEE Comput Intell Mag, 2013, 8: 39-51 CrossRef Google Scholar

[26] Xie L. Output feedback H control of systems with parameter uncertainty. Int J Control, 1996, 63: 741-750 CrossRef Google Scholar

[27] Luo Y Q, Wang Z D, Liang J L, et al. $H_{\infty} $ control for 2-D fuzzy systems with interval time-varying delays and missing measurements. IEEE Trans Cybern, 2017, 47: 365--377. Google Scholar

[28] Wang C, Ding Z. H consensus control of multi-agent systems with input delay and directed topology. IET Control Theor Appl, 2016, 10: 617-624 CrossRef Google Scholar

[29] Ding Z. Consensus Disturbance Rejection With Disturbance Observers. IEEE Trans Ind Electron, 2015, 62: 5829-5837 CrossRef Google Scholar

[30] Yang J, Ding Z, Chen W H. Output-based disturbance rejection control for non-linear uncertain systems with unknown frequency disturbances using an observer backstepping approach. IET Control Theor Appl, 2016, 10: 1052-1060 CrossRef Google Scholar

[31] Park M S, Chwa D, Eom M. Adaptive Sliding-Mode Antisway Control of Uncertain Overhead Cranes With High-Speed Hoisting Motion. IEEE Trans Fuzzy Syst, 2014, 22: 1262-1271 CrossRef Google Scholar

[32] Wu H N, Wang H D, Guo L. Finite dimensional disturbance observer based control for nonlinear parabolic PDE systems via output feedback. J Process Control, 2016, 48: 25-40 CrossRef Google Scholar

[33] Chen W H, Yang J, Guo L, et al. Disturbance observer-based control and related methods: an overview. IEEE Trans Ind Electron, 2015, 63: 1083--1095. Google Scholar

[34] Wang C, Zuo Z, Sun J. Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: A DOBC approach. J Franklin Institute, 2017, 354: 298-315 CrossRef Google Scholar

[35] Isidori A, Byrnes C I. Output regulation of nonlinear systems. IEEE Trans Automat Contr, 1990, 35: 131-140 CrossRef Google Scholar

[36] Ding Z. Output Regulation of Uncertain Nonlinear Systems With Nonlinear Exosystems. IEEE Trans Automat Contr, 2006, 51: 498-503 CrossRef Google Scholar

[37] Youfeng Su , Jie Huang . Cooperative Output Regulation With Application to Multi-Agent Consensus Under Switching Network. IEEE Trans Syst Man Cybern B, 2012, 42: 864-875 CrossRef PubMed Google Scholar

[38] Ding Z. Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems. IEEE Trans Automat Contr, 2013, 58: 2648-2653 CrossRef Google Scholar

[39] Ding Z. Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain. Automatica, 2015, 51: 348-355 CrossRef Google Scholar

[40] Ding Z. Distributed Adaptive Consensus Output Regulation of Network-Connected Heterogeneous Unknown Linear Systems on Directed Graphs. IEEE Trans Automat Contr, 2017, 62: 4683-4690 CrossRef Google Scholar

[41] Li Z, Ren W, Liu X. Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica, 2013, 49: 1986-1995 CrossRef Google Scholar

[42] Li Z, Wen G, Duan Z. Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs. IEEE Trans Automat Contr, 2015, 60: 1152-1157 CrossRef Google Scholar

[43] Sun J Y, Geng Z Y, Lv Y Z, et al. Distributed adaptive consensus disturbance rejection for multi-agent systems on directed graphs. IEEE Trans Control Netw Syst, 2016, doi: 10.1109/TCNS.2016.2641800. Google Scholar

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号