Abstract
This paper deals with the problem of cooperative control of time-delayed multi-agent systems. The objective is to achieve fixed-time regulation and reference tracking of multi-agent systems with a random time-delay in presence of external disturbances. In this work, an enhanced event-triggered distributed cooperative control technique is proposed for fixed-time consensus of multi-agent systems with random time-delay and external disturbances. The controller expression contains two terms: a term that ensures fixed-time consensus in absence of time-delay and a second term triggered by the delay detection, and that compensates in fixed time the time-delay effect. The main features of the controller designed in this work compared to the literature are: 1) It ensures reference tracking and regulation of time-delayed multi-agent systems before the desired pre-fixed maximum settling time, despite the random constant or variable time-delays and the external disturbances. 2) The pre-fixed maximum settling time is independent of the value of the time-delay. 3) Unlike conventional event-triggered control systems, in absence of the time-delay, the control signal is not maintained constant but only the time-delay compensating term is deactivated, and fixed-time consensus is still ensured by the remaining term of the controller expression. Comparative numerical case studies with fixed time and conventional asymptotic control are provided to highlight the efficiency of the proposed approach.
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Cao Y, Yu W, Ren W et al (2013) An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Industr Inf 9(1):427–438. https://doi.org/10.1109/TII.2012.2219061
Ding L, Han QL, Guo G (2013) Network-based leader-following consensus for distributed multi-agent systems. Automatica 49(7):2281–2286. https://doi.org/10.1016/j.automatica.2013.04.021
Djaidja S, Wu Q (2016) Leader-following consensus of single-integrator multi-agent systems under noisy and delayed communication. Int J Control Autom Syst 14(2):357–366. https://doi.org/10.1007/s12555-014-0262-6
Duan MM, Liu CL, Liu F (2016) Event-triggered consensus seeking of heterogeneous first-order multi-agent system. In: 2016 35th Chinese Control Conference (CCC), pp 7786–7791, https://doi.org/10.1109/ChiCC.2016.7554592
Ge X, Han QL (2017) Consensus of multiagent systems subject to partially accessible and overlapping markovian network topologies. IEEE Trans Cybern 47(8):1807–1819. https://doi.org/10.1109/TCYB.2016.2570860
Ge X, Han QL, Yang F (2017) Event-based set-membership leader-following consensus of networked multi-agent systems subject to limited communication resources and unknown-but-bounded noise. IEEE Trans Industr Electron 64(6):5045–5054. https://doi.org/10.1109/TIE.2016.2613929
He W, Zhang B, Han QL et al (2017) Leader-following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Trans Cybern 47(2):327–338. https://doi.org/10.1109/TCYB.2015.2514119
He X, Yang C, Li Z, et al. (2021) Consensus control for single-integrator multi-agent systems with unknown control directions via event-triggered approach. In: 2021 36th Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp 757–760, https://doi.org/10.1109/YAC53711.2021.9486554
Liu J, Yu Y, Xu Y et al (2022) Fixed-time average consensus of nonlinear delayed mass under switching topologies: an event-based triggering approach. IEEE Trans Syst Man Cybern Syst 52(5):2721–2733. https://doi.org/10.1109/TSMC.2021.3051156
Ni J, Liu L, Liu C et al (2017) Fixed-time leader-following consensus for second-order multiagent systems with input delay. IEEE Trans Industr Electron 64(11):8635–8646. https://doi.org/10.1109/TIE.2017.2701775
Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533. https://doi.org/10.1109/TAC.2004.834113
Qi T, Qiu L, Chen J (2017) Mas consensus and delay limits under delayed output feedback. IEEE Trans Autom Control 62(9):4660–4666. https://doi.org/10.1109/TAC.2016.2625422
Sun F, Tuo M, Kurths J et al (2020) Finite-time consensus of leader-following multi-agent systems with multiple time delays over time-varying topology. Int J Control Autom Syst 18(8):1985–1992. https://doi.org/10.1007/s12555-019-0266-3
Tian B, Lu H, Zuo Z et al (2019) Fixed-time leader-follower output feedback consensus for second-order multiagent systems. IEEE Trans Cybern 49(4):1545–1550. https://doi.org/10.1109/TCYB.2018.2794759
Wang A, Mu B, Shi Y (2019) Event-triggered consensus control for multiagent systems with time-varying communication and event-detecting delays. IEEE Trans Control Syst Technol 27(2):507–515. https://doi.org/10.1109/TCST.2017.2773537
Wang C, Tnunay H, Zuo Z et al (2019) Fixed-time formation control of multirobot systems: design and experiments. IEEE Trans Industr Electron 66(8):6292–6301. https://doi.org/10.1109/TIE.2018.2870409
Wang J, Peng Y, Dou L (2021) Mean square bipartite consensus for multi-agent systems with measurement noises and communication time-delays. Int J Control Autom Syst 19(12):3880–3889. https://doi.org/10.1007/s12555-020-0768-z
Wang YL, Han QL (2018) Network-based modelling and dynamic output feedback control for unmanned marine vehicles in network environments. Automatica 91:43–53. https://doi.org/10.1016/j.automatica.2018.01.026
Zhang L, Wang Y, Hou Y, et al. (2019) Fixed-time sliding mode control for uncertain robot manipulators. IEEE Access 7:149,750–149,763. https://doi.org/10.1109/ACCESS.2019.2946866
Zuo Z (2015) Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54:305–309. https://doi.org/10.1016/j.automatica.2015.01.021
Zuo Z, Yang W, Tie L, et al. (2014) Fixed-time consensus for multi-agent systems under directed and switching interaction topology. In: 2014 American Control Conference, pp 5133–5138, https://doi.org/10.1109/ACC.2014.6858741
Zuo Z, Han QL, Ning B et al (2018) An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Industr Inf 14(6):2322–2334. https://doi.org/10.1109/TII.2018.2817248
Zuo Z, Tian B, Defoort M et al (2018) Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Trans Autom Control 63(2):563–570. https://doi.org/10.1109/TAC.2017.2729502
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Ghazzali, M., Haloua, M. & Giri, F. An enhanced event-triggered distributed fixed-time controller for multi-agent systems with random time-delays. Int. J. Dynam. Control 12, 1571–1581 (2024). https://doi.org/10.1007/s40435-023-01271-w
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DOI: https://doi.org/10.1007/s40435-023-01271-w