Semi-global leader-following output consensus of heterogeneous systems subject to actuator position and rate saturation

Abstract

We study in this paper a semi-global leader-following output consensus problem for multiple heterogeneous linear systems in the presence of actuator position and rate saturation over a directed topology. For each follower, via the low gain feedback design technique and output regulation theory, both a state feedback consensus protocol and an output feedback consensus protocol are constructed. In the output feedback case, different distributed observers are designed for the informed followers and uninformed followers to estimate the state of the leader and the follower itself. We show that the semi-global leader-following output consensus of heterogeneous linear systems can be achieved by the two consensus protocols if each follower is reachable from the leader in the directed communication topology.

Keywords

Multi-agent system / Output consensus / Low gain feedback

References

[1] RadenkovićM. S., KrstićM.. Distributed adaptive consensus and synchronization in complex networks of dynamical systems. Automatica, 2018, 91: 233-243

[2] WangY., SongY., KrstićM., WenC.. Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directed communication interactions and actuation failures. Automatica, 2016, 63: 374-383

[3] MengH., ChenZ., MiddletonR.. Consensus of multiagents in switching networks using input-to-state stability of switched systems. IEEE Trans. Autom. Control., 2018, 63(11):3964-3971

[4] LiD., GeS. S., LeeT.. Fixed-time-synchronized consensus control of multi-agent systems. IEEE Trans Control. Netw. Syst., 2020, 8(1):89-98

[5] DongS., RenW., WuZ.. Observer-based distributed mean-square consensus design for leader-following multiagent markov jump systems. IEEE Trans. Cybern., 2021, 51(6):3054-3061

[6] LuM., LiuL.. Leader-following attitude consensus of multiple rigid spacecraft systems under switching networks. IEEE Trans. Autom. Control., 2019, 65(2):839-845

[7] LiZ., RenW., LiuX., XieL.. Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica, 2013, 49(7):1986-1995

[8] LiZ., WenG., DuanZ., RenW.. Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs. IEEE Trans. Autom. Control., 2014, 60(4):1152-1157

[9] MaQ., MiaoG.. Output consensus for heterogeneous multi-agent systems with linear dynamics. Appl. Math. Comput., 2015, 271: 548-555

[10] HanT., GuanZ., XiaoB., WuJ., ChenX.. Distributed output consensus of heterogeneous multi-agent systems via an output regulation approach. Neurocomputing, 2019, 360: 131-137

[11] LiuY., MinH., WangS., LiuZ., LiaoS.. Distributed consensus of a class of networked heterogeneous multi-agent systems. J. Frankl. Inst., 2014, 351(3):1700-1716

[12] LiuT., HuangJ.. A distributed observer for a class of nonlinear systems and its application to a leader-following consensus problem. IEEE Trans. Autom. Control., 2018, 64(3):1221-1227

[13] YuY., LiZ., YangZ., DingZ.. Distributed back-stepping consensus protocol for attitude synchronization and tracking on undirected graphs. Unmanned Syst., 2019, 7(1):25-32

[14] YangT., MengZ., DimarogonasD. V., JohanssonK. H.. Global consensus for discrete-time multi-agent systems with input saturation constraints. Automatica, 2014, 50(2):499-506

[15] L. Shi, Z. Lin, in Proceedings of the 37th Chinese Control Conference. Semi-global output containment control of linear multi-agent systems with actuator saturation, (2018), pp. 7160–7165.

[16] QinJ., FuW., ZhengW., GaoH.. On the bipartite consensus for generic linear multiagent systems with input saturation. IEEE Trans. Cybern., 2016, 47(8):1948-1958

[17] ShiL., LiY., LinZ.. Semi-global leader-following output consensus of heterogeneous multi-agent systems with input saturation. Int. J. Robust Nonlinear Control., 2018, 28(16):4916-4930

[18] L. Shi, Y. Li, Z. Lin, in Proceedings of the 2018 IEEE International Conference on Real-time Computing and Robotics. Semi-global leader-following output consensus of discrete-time linear multi-agent systems with input saturation, (2018), pp. 354–359.

[19] L. Shi, Y. Li, Z. Lin, in Proceedings of the 15th IEEE International Conference on Control and Automation. Semi-global output containment control for a group of heterogeneous discrete-time linear systems with input saturation, (2019), pp. 1138–1143.

[20] LinZ.. Low Gain Feedback, 1999 London Springer-Verlag

[21] ZhengY., ZhuY., WangL.. Consensus of heterogeneous multi-agent systems. IET Control. Theory Appl., 2011, 5(16):1881-1888

[22] MengZ., ZhaoZ., LinZ.. On global leader-following consensus of identical linear dynamic systems subject to actuator saturation. Syst. Control Lett., 2013, 62(2):132-142

[23] Y. Xie, Z. Lin, in Proceedings of the 2019 Chinese Control Conference. Global consensus of multi-agent systems with intermittent directed communication in the presence of actuator saturation, (2019), pp. 5958–5963.

[24] DornheinM.. Report pinpoints factors leading to YF-22 crash. Aviat. Week Space Technol., 1992, 9: 53-54

[25] LinZ.. Semi-global stabilization of linear systems with position and rate-limited actuators. Syst. Control Lett., 1997, 30(1):1-11

[26] LimY., AhnH. S.. Decentralized control of nonlinear interconnected systems under both amplitude and rate saturations. Automatica, 2013, 49(8):2551-2555

[27] ZhaoZ., LinZ.. Semi-global leader-following consensus of multiple linear systems with position and rate limited actuators. Int. J. Robust Nonlinear Control., 2015, 25(13):2083-2100

[28] ZhaoZ., ShiH.. Semi-global containment control for linear systems in the presence of actuator position and rate saturation. Int. J. Robust Nonlinear Control., 2019, 29(1):1-18

[29] Z. Lin, M. Pachter, S. Banda, Y. Shamash, in Guidance, Navigation, and Control Conference. Feedback design for robust tracking of linear systems with rate limited actuators, (1997), p. 3609.

[30] HongY., WangX., JiangZ.. Distributed output regulation of leader–follower multi-agent systems. Int. J. Robust Nonlinear Control., 2013, 23(1):48-66

[31] LiZ., RenW., LiuX., FuM.. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int. J. Robust Nonlinear Control., 2013, 23(5):534-547

[32] P. Zhou, B. M. Chen, in Proceedings of the 2021 Chinese Control Conference. Semi-global leader-following output consensus of heterogeneous systems with position and rate-limited actuators via state feedback, (2021), pp. 5295–5302.

Funding

Research Grants Council of Hong Kong SAR(14209020)