Abstract
This paper deals with the problem of output containment control of heterogeneous linear multi-agent systems. The objective is to design a distributed control law that drives the output of heterogeneous linear multi-agent systems to the dynamic convex hull spanned by the leaders. To do this, a sliding-mode distributed output containment controller is proposed in this work. We consider a general network topology which only contains a united spanning tree with no assumptions made regarding the topology as long as its stationary or quasi-stationary. The dynamics of the leaders are considered unknown, and only their outputs, i.e., the references, are available. The designed method has several advantages compared to the existing literature: (1) exponential convergence of the output containment error to zero within a response time fixed in advance; (2) control law with simple mathematical expression and thus easy numerical implementation; (3) easy and straightforward design procedure; (4) easy controller tuning, as the controller has one tuning parameter only; and (5) robustness to external disturbances without requiring additional signals in the control law for this purpose. A numerical example is provided to highlight the efficiency of the proposed approach under external disturbances.
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References
Cheema, M. A. M., Fletcher, J. E., Farshadnia, M., et al. (2017). Combined speed and direct thrust force control of linear permanent-magnet synchronous motors with sensorless speed estimation using a sliding-mode control with integral action. IEEE Transactions on Industrial Electronics, 64(5), 3489–3501. https://doi.org/10.1109/TIE.2017.2652368
Cheema, M. A. M., Fletcher, J. E., Farshadnia, M., et al. (2019). Sliding mode based combined speed and direct thrust force control of linear permanent magnet synchronous motors with first-order plus integral sliding condition. IEEE Transactions on Power Electronics, 34(3), 2526–2538. https://doi.org/10.1109/TPEL.2018.2839060
Chu, H., Gao, L., & Zhang, W. (2016). Distributed adaptive containment control of heterogeneous linear multi-agent systems: An output regulation approach. IET Control Theory & Applications, 10(1), 95–102. https://doi.org/10.1049/iet-cta.2015.0398
Ferrara, A., & Incremona, G. P. (2015). Design of an integral suboptimal second-order sliding mode controller for the robust motion control of robot manipulators. IEEE Transactions on Control Systems Technology, 23(6), 2316–2325. https://doi.org/10.1109/TCST.2015.2420624
Fu, J., Wan, Y., Wen, G., et al. (2019). Distributed robust global containment control of second-order multiagent systems with input saturation. IEEE Transactions on Control of Network Systems, 6(4), 1426–1437. https://doi.org/10.1109/TCNS.2019.2893665
Gong, X., Cui, Y., Shen, J., et al. (2022). Necessary and sufficient conditions of formation-containment control of high-order multiagent systems with observer-type protocols. IEEE Transactions on Cybernetics, 52(7), 7002–7016. https://doi.org/10.1109/TCYB.2020.3037133
Guzman, R., de Vicuña, L. G., Morales, J., et al. (2016). Sliding-mode control for a three-phase unity power factor rectifier operating at fixed switching frequency. IEEE Transactions on Power Electronics, 31(1), 758–769. https://doi.org/10.1109/TPEL.2015.2403075
Hamed, H., Mohammad Ali, B., & Mahdi, B. (2015). Containment control of heterogeneous linear multi-agent systems. Automatica, 54, 210–216. https://doi.org/10.1016/j.automatica.2015.02.002
Huang, W., Liu, H., & Huang, J. (2022). Distributed robust containment control of linear heterogeneous multi-agent systems: an output regulation approach. IEEE/CAA Journal of Automatica Sinica, 9(5), 864–877. https://doi.org/10.1109/JAS.2022.105560
Huang, Y., Zhang, Z., Huang, W., et al. (2019). DC-link voltage regulation for wind power system by complementary sliding mode control. IEEE Access, 7, 22773–22780. https://doi.org/10.1109/ACCESS.2019.2898997
Khanzadeh, A., & Pourgholi, M. (2018). Fixed-time leader–follower consensus tracking of second-order multi-agent systems with bounded input uncertainties using non-singular terminal sliding mode technique. IET Control Theory Applications, 12(5), 679–686. https://doi.org/10.1049/iet-cta.2017.1094
Li, H., Zhu, M., Chu, Z., et al. (2018). Fixed-time synchronization of a class of second-order nonlinear leader-following multi-agent systems. Asian Journal of Control, 20(1), 39–48. https://doi.org/10.1002/asjc.1585
Ling, R., Maksimovic, D., & Leyva, R. (2016). Second-order sliding-mode controlled synchronous buck DC–DC converter. IEEE Transactions on Power Electronics, 31(3), 2539–2549. https://doi.org/10.1109/TPEL.2015.2431193
Liu, H., Xie, G., & Wang, L. (2012). Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica, 48(7), 1415–1422. https://doi.org/10.1016/j.automatica.2012.05.010
Liu, J., Yin, Y., Luo, W., et al. (2018). Sliding mode control of a three-phase AC/DC voltage source converter under unknown load conditions: industry applications. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48(10), 1771–1780. https://doi.org/10.1109/TSMC.2017.2758598
Liu, J., Yu, Y., Xu, Y., et al. (2021). Fixed-time average consensus of nonlinear delayed mass under switching topologies: An event-based triggering approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems.https://doi.org/10.1109/TSMC.2021.3051156
Meng, D., & Jia, Y. (2016). Robust consensus algorithms for multiscale coordination control of multivehicle systems with disturbances. IEEE Transactions on Industrial Electronics, 63(2), 1107–1119. https://doi.org/10.1109/TIE.2015.2478740
Merabet, A., Labib, L., Ghias, A. M. Y. M., et al. (2017). Robust feedback linearizing control with sliding mode compensation for a grid-connected photovoltaic inverter system under unbalanced grid voltages. IEEE Journal of Photovoltaics, 7(3), 828–838. https://doi.org/10.1109/JPHOTOV.2017.2667724
Nair, R. R., Karki, H., Shukla, A., et al. (2019). Fault-tolerant formation control of nonholonomic robots using fast adaptive gain nonsingular terminal sliding mode control. IEEE Systems Journal, 13(1), 1006–1017. https://doi.org/10.1109/JSYST.2018.2794418
Ni, J., Liu, L., Liu, C., et al. (2017). Fixed-time leader-following consensus for second-order multiagent systems with input delay. IEEE Transactions on Industrial Electronics, 64(11), 8635–8646. https://doi.org/10.1109/TIE.2017.2701775
Notarstefano, G., Egerstedt, M., & Haque, M. (2011). Containment in leader–follower networks with switching communication topologies. Automatica, 47(5), 1035–1040. https://doi.org/10.1016/j.automatica.2011.01.077
Qi, W., Li, S., Tan, S. C., et al. (2018). Parabolic-modulated sliding-mode voltage control of a buck converter. IEEE Transactions on Industrial Electronics, 65(1), 844–854. https://doi.org/10.1109/TIE.2017.2716859
Qin, J., Ma, Q., Yu, X., et al. (2019). Output containment control for heterogeneous linear multiagent systems with fixed and switching topologies. IEEE Transactions on Cybernetics, 49(12), 4117–4128. https://doi.org/10.1109/TCYB.2018.2859159
Tian, B., Lu, H., Zuo, Z., et al. (2018). Fixed-time leader–follower output feedback consensus for second-order multiagent systems. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2018.2794759
Tian, B., Lu, H., Zuo, Z., et al. (2019). Fixed-time leader–follower output feedback consensus for second-order multiagent systems. IEEE Transactions on Cybernetics, 49(4), 1545–1550. https://doi.org/10.1109/TCYB.2018.2794759
Van, M., Mavrovouniotis, M., & Ge, S. S. (2019). An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(7), 1448–1458. https://doi.org/10.1109/TSMC.2017.2782246
Villanueva, I., Rosales, A., Ponce, P., et al. (2018). Grid-voltage-oriented sliding mode control for DFIG under balanced and unbalanced grid faults. IEEE Transactions on Sustainable Energy, 9(3), 1090–1098. https://doi.org/10.1109/TSTE.2017.2769062
Wang, C., Tnunay, H., Zuo, Z., et al. (2019). Fixed-time formation control of multirobot systems: Design and experiments. IEEE Transactions on Industrial Electronics, 66(8), 6292–6301. https://doi.org/10.1109/TIE.2018.2870409
Wang, F., Liu, Z., & Chen, Z. (2020). Delay-induced containment control of second-order multi-agent systems with intermittent sampled position data. IEEE Access, 8, 20334–20341. https://doi.org/10.1109/ACCESS.2020.2969243
Wang, H., Pan, Y., Li, S., et al. (2019). Robust sliding mode control for robots driven by compliant actuators. IEEE Transactions on Control Systems Technology, 27(3), 1259–1266. https://doi.org/10.1109/TCST.2018.2799587
Wang, Q., Yu, H., Wang, M., et al. (2019). An improved sliding mode control using disturbance torque observer for permanent magnet synchronous motor. IEEE Access, 7, 36691–36701. https://doi.org/10.1109/ACCESS.2019.2903439
Wang, X., Li, S., & Shi, P. (2014). Distributed finite-time containment control for double-integrator multiagent systems. IEEE Transactions on Cybernetics, 44(9), 1518–1528. https://doi.org/10.1109/TCYB.2013.2288980
Wang, X., Reitz, M., & Yaz, E. E. (2018). Field oriented sliding mode control of surface-mounted permanent magnet AC motors: Theory and applications to electrified vehicles. IEEE Transactions on Vehicular Technology, 67(11), 10343–10356. https://doi.org/10.1109/TVT.2018.2865905
Wen, G., Zhao, Y., Duan, Z., et al. (2016). Containment of higher-order multi-leader multi-agent systems: A dynamic output approach. IEEE Transactions on Automatic Control, 61(4), 1135–1140. https://doi.org/10.1109/TAC.2015.2465071
Yang, Q., Saeedifard, M., & Perez, M. A. (2019). Sliding mode control of the modular multilevel converter. IEEE Transactions on Industrial Electronics, 66(2), 887–897. https://doi.org/10.1109/TIE.2018.2818657
Zhang, R., & Hredzak, B. (2019). Nonlinear sliding mode and distributed control of battery energy storage and photovoltaic systems in AC microgrids with communication delays. IEEE Transactions on Industrial Informatics, 15(9), 5149–5160. https://doi.org/10.1109/TII.2019.2896032
Zhang, X., Yu, M., & Liranso, D. D. (2019). Containment of linear multi-agent systems with multiple leaders of bounded input and exogenous disturbances. In 2019 Chinese control and decision conference (CCDC) (pp. 3448–3452). https://doi.org/10.1109/CCDC.2019.8833369
Zuo, S., Song, Y., Lewis, F. L., et al. (2017). Output containment control of linear heterogeneous multi-agent systems using internal model principle. IEEE Transactions on Cybernetics, 47(8), 2099–2109. https://doi.org/10.1109/TCYB.2016.2641394
Zuo, Z., Han, Q. L., Ning, B., et al. (2018). An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Transactions on Industrial Informatics, 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 Transactions on Automatic Control, 63(2), 563–570. https://doi.org/10.1109/TAC.2017.2729502
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Ghazzali, M., Haloua, M. & Giri, F. Sliding-Mode Distributed Output Containment Control for Heterogeneous Linear Multi-agent Systems with Multiple Leaders with Unknown Dynamics. J Control Autom Electr Syst 34, 941–950 (2023). https://doi.org/10.1007/s40313-023-01018-0
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DOI: https://doi.org/10.1007/s40313-023-01018-0