Prescribed-Time Group-Bipartite Consensus for Second-Order Nonlinear Multi-Agent Systems

Abstract

The problem of prescribed-time group-bipartite leader-follower consensus for second-order nonlinear multi-agent systems (MASs) is investigated over a signed communication topology. First, by selecting a time-varying function as the control gain, we propose a novel control protocol for the case where each sub-topology is structurally balanced. By introducing an additional gain parameter into the controller, we simplify the sufficient conditions for the stability of the closed-loop system, and the calculations of parameters are more straightforward. Second, by incorporating leader dynamics into the controller, we relax the topological constraints and only require the overall topology of the MAS to be structurally balanced, and propose a novel consensus protocol based on neighbor information and leader dynamics. Based on matrix theory and Lyapunov stability theory, we derive sufficient conditions for achieving consensus. Finally, two numerical simulation examples are provided to validate the effectiveness of the two control protocols.

Keywords

group-bipartite consensus / multi-agent system (MAS) / prescribed-time / signed graph

References

[1] Xue D, Yao J, Chen G, et al. Formation control of networked multi—agent systems[J]. IET Control Theory & Applications, 2010, 4(10): 2168-2176.

[2] Yu W W, Chen G R, Wang Z D, et al. Distributed consensus filtering in sensor networks[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2009, 39(6): 1568-1577.

[3] Chen S M, Pei H Q, Lai Q, et al. Multitarget tracking control for coupled heterogeneous inertial agents systems based on flocking behavior[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(12): 2605-2611.

[4] Chen C, Lewis F L, Li X L. Event—triggered coordination of multi—agent systems via a Lyapunov—based approach for leaderless consensus[J]. Automatica, 2022, 136: 109936.

[5] Zhou T H, Zhai S D, Li C Y, et al. Fully distributed leaderless consensus of general nonlinear multi—agent systems with directed topology and bounded disturbances[J]. IAENG International Journal of Applied Mathematics, 2024, 54(1): 40-46.

[6] Liu X Y, Sun J, Dou L H, et al. Leader—following consensus for discrete—time multi—agent systems with parameter uncertainties based on the event—triggered strategy[J]. Journal of Systems Science and Complexity, 2017, 30(1): 30-45.

[7] Li G L, Ren C E, Philip Chen C L. Preview—based leader—following consensus control of distributed multi—agent systems[J]. Information Sciences, 2021, 559: 251-269.

[8] Zheng Z H, Pan J P, Cai L. Lightweight blockchain consensus protocols for vehicular social networks[J]. IEEE Transactions on Vehicular Technology, 2020, 69(6): 5736-5748.

[9] Wu T, Liu X W, Qin J D, et al. Trust—consensus multiplex networks by combining trust social network analysis and consensus evolution methods in group decision—making[J]. IEEE Transactions on Fuzzy Systems, 2022, 30(11): 4741-4753.

[10] Altafini C. Consensus problems on networks with antagonistic interactions[J]. IEEE Transactions on Automatic Control, 2013, 58(4): 935-946.

[11] Ma C Q, Qin Z Y. Bipartite consensus on networks of agents with antagonistic interactions and measurement noises[J]. IET Control Theory & Applications, 2016, 10(17): 2306-2313.

[12] Yang R T, Peng L, Yang Y Q, et al. Bipartite consensus of linear multi—agent systems by distributed event—triggered control[J]. Journal of Systems Science and Complexity, 2021, 34(3): 955-974.

[13] Zhang X X, Han W Y, Liu X P. Bipartite tracking consensus of linear multi—agent systems with a dynamic leader under signed digraph[J]. IET Control Theory & Applications, 2020, 14(15): 2127-2133.

[14] Yu J Y, Wang L. Group consensus of multi—agent systems with directed information exchange[J]. International Journal of Systems Science, 2012, 43(2): 334-348.

[15] Qin J H, Yu C B. Cluster consensus control of generic linear multi—agent systems under directed topology with acyclic partition[J]. Automatica, 2013, 49(9): 2898-2905.

[16] Xia H, Huang T Z, Shao J L, et al. Group consensus of multi—agent systems with communication delays[J]. Neurocomputing, 2016, 171: 1666-1673.

[17] Liu J, Li H Y, Ji J C, et al. Group—bipartite consensus in the networks with cooperative—competitive interactions[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2020, 67(12): 3292-3296.

[18] Liu C, Li R, Liu B. Group—bipartite consensus of heterogeneous multi—agent systems over signed networks[J]. Physica A: Statistical Mechanics and its Applications, 2022, 592: 126712.

[19] Lu R X, Wu J, Zhan X S, et al. Finite—time group—bipartite consensus tracking for second—order nonlinear multi—agent systems[J]. Neurocomputing, 2023, 545: 126283.

[20] Zhou Y Y, Zhang G S. Distributed finite—time lag—consensus for second—order nonlinear multi—agent systems with disturbances[C]// 2018 13th World Congress on Intelligent Control and Automation (WCICA). Piscataway, NJ: IEEE, 2019: 1594-1599.

[21] Hao L L, Zhan X S, Wu J, et al. Fixed—time group consensus of nonlinear multi—agent systems via pinning control[J]. International Journal of Control, Automation and Systems, 2021, 19(1): 200-208.

[22] Ren Y H, Zhou W N, Li Z W, et al. Prescribed—time cluster lag consensus control for second—order non—linear leader—following multiagent systems[J]. ISA Transactions, 2021, 109: 49-60.

[23] Ning B D, Han Q L, Zuo Z Y. Bipartite consensus tracking for second—order multiagent systems: a time—varying function—based preset—time approach[J]. IEEE Transactions on Automatic Control, 2021, 66(6): 2739-2745.

[24] Zhao Y, Zhou Y, Huang P F, et al. Appointed—time and attack—free bipartite synchronization of generic linear multiagent systems over directed switching networks[J]. IEEE Transactions on Automatic Control, 2022, 67(9): 4498-4513.

[25] Lv J X, Wang C H, Liu B, et al. Fully distributed prescribed—time consensus control of multiagent systems under fixed and switching topologies[J]. Information Sciences, 2023, 648: 119538.

[26] Qu Z H. Cooperative control of dynamical systems: applications to autonomous vehicles[M]. London: Springer Science & Business Media, 2009.

[27] Horn R A, Johnson C R. Matrix analysis[M]. 2nd ed. Cambridge, UK: Cambridge University Press, 2012.