Abstract
In this paper, a class of disturbed networked Euler-Lagrangian systems is investigated to track a general virtual signal under a general directed communication network. Firstly, a class of fixed-time distributed observer is constructed to estimate the leader’s state. Secondly, a local anti-disturbance tracking control based on the previous distributed observer is proposed for each follower to achieve the tracking consensus in a fixed time. A simulation example is finally conducted to verify the proposed algorithm.
Similar content being viewed by others
References
Yu W, Wen G, Chen G, et al. Distributed Cooperative Control of Multi-Agent Systems. Singapore: Wiley, 2017
Ding L, Wang L Y, Yin G Y, et al. Distributed energy management for smart grids with an event-triggered communication scheme. IEEE Trans Contr Syst Technol, 2019, 27: 1950–1961
Zhang M, Shen C, He N, et al. False data injection attacks against smart gird state estimation: Construction, detection and defense. Sci China Tech Sci, 2019, 62: 2077–2087
Zhang J, Yan J, Zhang P, et al. Collision avoidance in fixed-wing UAV formation flight based on a consensus control algorithm. IEEE Access, 2018, 6: 43672–43682
Chen L, Hopman H, Negenborn R R. Distributed model predictive control for vessel train formations of cooperative multi-vessel systems. Transpation Res Part C-Emerging Technol, 2018, 92: 101–118
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
Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr, 2005, 50: 655–661
Wang L J, Meng B. Characteristic model-based consensus of networked heterogeneous robotic manipulators with dynamic uncertainties. Sci China Tech Sci, 2016, 59: 63–71
Hu H X, Zhou Q, Wen G, et al. Robust distributed stabilization of heterogeneous agents over cooperation-competition networks. IEEE Trans Circuits Syst II, 2019, doi: https://doi.org/10.1109/TCSII.2019.2933578
Cao Y, Yu W, Ren W, et al. An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Ind Inf, 2013, 9: 427–438
Zhou J, Wu X J, Liu Z R. Distributed coordinated adaptive tracking in networked redundant robotic systems with a dynamic leader. Sci China Tech Sci, 2014, 57: 905–913
Xu Y, Li D Y, Luo D L, et al. Affine formation maneuver tracking control of multiple second-order agents with time-varying delays. Sci China Tech Sci, 2019, 62: 665–676
Ji M, Ferrari-Trecate G, Egerstedt M, et al. Containment control in mobile networks. IEEE Trans Automat Contr, 2008, 53: 1972–1975
Yu W W, Chen G R, Cao M, et al. Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern B, 2010, 40: 881–891
Wang L, Xiao F. Finite-time consensus problems for networks of dynamic agents. IEEE Trans Automat Contr, 2010, 55: 950–955
Cao Y C, Ren W. Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans Automat Contr, 2012, 57: 33–48
Cortés J. Finite-time convergent gradient flows with applications to network consensus. Automatica, 2006, 42: 1993–2000
Hong H, Wang H, Wang Z, et al. Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information. Sci China Inf Sci, 2019, 62: 212201
Liu K X, Wu L L, Lü J H, et al. Finite-time adaptive consensus of a class of multi-agent systems. Sci China Tech Sci, 2016, 59: 22–32
Polyakov A. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Automat Contr, 2012, 57: 2106–2110
Hong H, Yu W, Wen G, et al. Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems. IEEE Trans Syst Man Cybern Syst, 2017, 47: 1464–1473
Zuo Z. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 2015, 54: 305–309
Zhao Y, Liu Y, Wen G, et al. Designing distributed specified-time consensus protocols for linear multiagent systems over directed graphs. IEEE Trans Automat Contr, 2019, 64: 2945–2952
Wang Y, Song Y. Leader-following control of high-order multi-agent systems under directed graphs: Pre-specified finite time approach. Automatica, 2018, 87: 113–120
Ren W. Distributed leaderless consensus algorithms for networked Euler-Lagrange systems. Int J Control, 2009, 82: 2137–2149
Huang N, Duan Z S, Zhao Y. Distributed consensus for multiple Euler-Lagrange systems: An event-triggered approach. Sci China Tech Sci, 2016, 59: 33–44
Hu H X, Wen G, Yu W, et al. Swarming behavior of multiple euler-lagrange systems with cooperation-competition interactions: An auxiliary system approach. IEEE Trans Neural Netw Learning Syst, 2018, 29: 5726–5737
He W, Xu C, Han Q L, et al. Finite-time ℒ2 leader-follower consensus of networked Euler-Lagrange systems with external disturbances. IEEE Trans Syst Man Cybern Syst, 2018, 48: 1920–1928
Zhao Y, Duan Z, Wen G. Distributed finite-time tracking of multiple Euler-Lagrange systems without velocity measurements. Int J Robust Nonlinear Control, 2015, 25: 1688–1703
Ni J, Liu L, Liu C, et al. Fixed-time leader-following consensus for second-order multiagent systems with input delay. IEEE Trans Ind Electron, 2017, 64: 8635–8646
Yang Y, Hua C, Li J, et al. Fixed-time coordination control for bilateral telerobotics system with asymmetric time-varying delays. J Intell Robot Syst, 2017, 86: 447–466
Godsil C, Royle G F. Algebraic Graph Theory. New York: Springer Science & Business Media, 2013
Li Z, Liu X, Ren W, et al. Distributed tracking control for linear multiagent systems with a leader of bounded unknown input. IEEE Trans Automat Contr, 2013, 58: 518–523
Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences. New York: Academic Press, 1979
Basin M, Shtessel Y, Aldukali F. Continuous finite- and fixed-time high-order regulators. J Franklin Inst, 2016, 353: 5001–5012
Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 2012
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grant No. 11601077), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20160662).
Rights and permissions
About this article
Cite this article
Yao, L., Wang, H. Designing fixed-time tracking consensus protocols for networked Euler-Lagrangian systems with directed graphs. Sci. China Technol. Sci. 63, 1846–1853 (2020). https://doi.org/10.1007/s11431-019-1566-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-019-1566-9