access icon free Leader–following consensus problem of networked multi-agent systems under switching topologies and communication constraints

© The Institution of Engineering and Technology
Received 31/07/2020, Accepted 04/01/2021, Revised 26/11/2020, Published 11/03/2021

The problem of leader–following consensus is investigated for heterogeneous discrete-time linear networked multi-agent systems with data packet losses and network delays. Two kinds of networked protocols are presented to derive the states of followers to reach an agreement on leader's state under the switching topologies, in the meanwhile, the asymptotic stability of all agents are guaranteed. Due to unavailable agents' states and communication constraints, the networked predictive control method is used to compensate network delays and data packet losses actively. Sufficient criteria of leader–following consensus and asymptomatic stability are obtained when at least one follower is connected to the leader by a directed edge. The simulation example is presented to illustrate that states of followers can track leader's state, and all agents' states also asymptotically converge to the equilibrium under the proposed theoretical results.

Inspec keywords: discrete time systems; topology; linear systems; multi-agent systems; networked control systems; multi-robot systems; asymptotic stability; delays; predictive control; stability; distributed control

Other keywords: network delays; networked protocols; networked predictive control method; communication constraints; data packet losses; asymptotic stability; leader–following consensus problem; discrete-time linear networked multiagent systems; switching topologies; unavailable agents

Subjects: Linear control systems; Multivariable control systems; Stability in control theory; Optimal control; Discrete control systems; Distributed parameter control systems; Control system analysis and synthesis methods

References

    1. 1)
      • 1. Wei, R.: ‘On consensus algorithms for double-integrator dynamics’, IEEE Trans. Autom. Control, 2008, 53, (6), pp. 1503–1509.
    2. 2)
      • 12. Zhang, J., Zhang, H., Lu, Y., et al: ‘Event∖self-triggered leader-following consensus of multi-agent systems with general dynamics’, IET Control Theory Appl., 2020, 14, pp. 1209–1219.
    3. 3)
      • 24. Mahmoud, M.S., Khan, G.D.: ‘Leader-following discrete consensus control of multi-agent systems with fixed and switching topologies’, J. Franklin Inst., 2015, 352, (6), pp. 2504–2525.
    4. 4)
      • 27. Tang, Y.: ‘Coordination of multi-agent systems under switching topologies via disturbance observer based approach’, Int. J. Syst. Sci., 2016, 47, pp. 3900–3907.
    5. 5)
      • 17. Zheng, T., He, M., Xi, J., et al: ‘Leader-following guaranteed-performance consensus design for singular multi-agent systems with Lipschitz nonlinear dynamics’, Neurocomputing, 2017, 266, pp. 651–658.
    6. 6)
      • 33. Hespanha, J.P.: ‘Uniform stability of switched linear systems: extensions of LaSalle's invariance principle’, IEEE Trans. Autom. Control, 2004, 49, (4), pp. 470–482.
    7. 7)
      • 42. Jiang, Y., Liu, J., Wang, S.: ‘Cooperative output feedback tracking control for multi-agent consensus with time-varying delays and switching topology’, Trans. Inst. Meas. Control, 2015, 37, (4), pp. 550–559.
    8. 8)
      • 6. Ma, Z., Liu, Z., Chen, Z.: ‘Leader-following consensus of multi-agent system with a smart leader’, Neurocomputing, 2016, 214, pp. 401–408.
    9. 9)
      • 47. Tan, C., Liu, G.P.: ‘Consensus of discrete-time linear networked multi-agent systems with communication delays’, IEEE Trans. Autom. Control, 2013, 58, (11), pp. 2962–2968.
    10. 10)
      • 19. Hong, Y., Chen, G., Bushnell, L.: ‘Distributed observers design for leader-following control of multi-agent networks’, Automatica, 2008, 44, (3), pp. 846–850.
    11. 11)
      • 50. Boyd, S., El-Ghaoui, L., Feron, E., et al: ‘Linear matrix inequalities in system and control theory’. studies in applied mathematics.' (SIAM, Philadelphia, PA, 1994).
    12. 12)
      • 13. Wen, G., Peng, Z., Rahmani, A., et al: ‘Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics’, Int. J. Syst. Sci., 2014, 45, pp. 1892–1901.
    13. 13)
      • 39. Yu, S., Yu, Z., Jiang, H., et al: ‘Leader-following guaranteed performance consensus for second-order multi-agent systems with and without communication delays’, IET Control Theory Appl., 2018, 12, (15), pp. 2055–2066.
    14. 14)
      • 5. Hong, Y., Hu, J., Gao, L.: ‘Tracking control for multi-agent consensus with an active leader and variable topology’, Automatica, 2006, 42, (7), pp. 1177–1182.
    15. 15)
      • 25. Xu, X., Chen, S., Huang, W., et al: ‘Leader-following consensus of discrete-time multi-agent systems with observer-based protocols’, Neurocomputing, 2013, 118, pp. 334–341.
    16. 16)
      • 26. Song, G., Tao, G.: ‘Adaptive leader-following state consensus of multiagent systems with switching topology’, Int. J. Adapt. Control Signal Process., 2018, 32, pp. 1508–1528.
    17. 17)
      • 38. Olfati-Saber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520–1533.
    18. 18)
      • 40. Zhu, W.: ‘Consensus of multiagent systems with switching jointly reachable interconnection and time delays’, IEEE Trans. Syst. Man Cybern. A, Syst. Humans, 2012, 42, (2), pp. 348–358.
    19. 19)
      • 28. Jia, Q., Tang, W.K.S., Halang, W.A.: ‘Leader following of nonlinear agents with switching connective network and coupling delay’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2011, 58, (10), pp. 2508–2519.
    20. 20)
      • 14. Song, Q., Cao, J., Yu, W.: ‘Second-order leader-following consensus of nonlinear multi-agent systems via pinning control’, Syst. Control Lett., 2010, 59, (9), pp. 553–562.
    21. 21)
      • 37. Yuan, S., De-Schutter, B., Baldi, S.: ‘Adaptive asymptotic tracking control of uncertain time-driven switched linear systems’, IEEE Trans. Autom. Control, 2017, 62, (11), pp. 5802–5807.
    22. 22)
      • 31. Atrianfar, H., Haeri, M.: ‘Adaptive flocking control of nonlinear multi-agent systems with directed switching topologies and saturation constraints’, J. Franklin Inst.-Eng. Appl. Math., 2013, 350, (6), pp. 1545–1561.
    23. 23)
      • 44. Cui, B., Zhao, C., Ma, T., et al: ‘Leaderless and leader-following consensus of multi-agent chaotic systems with unknown time delays and switching topologies’, Nonlinear Anal. Hybrid Syst., 2017, 24, pp. 115–131.
    24. 24)
      • 7. Yang, H.Y., Zhu, X.L., Zhang, S.Y.: ‘Consensus of second-order delayed multi-agent systems with leader-following’, Eur. J. Control, 2010, 16, pp. 188–199.
    25. 25)
      • 49. Tan, C., Yue, L., Li, Y., et al: ‘Group consensus control for discrete-time heterogeneous multi-agent systems with time delays’, Neurocomputing, 2020, 392, (7), pp. 70–85.
    26. 26)
      • 30. Cai, Y., Zhang, H., Zhang, K., et al: ‘Distributed leader-following consensus of heterogeneous second-order time-varying nonlinear multi-agent systems under directed switching topology’, Neurocomputing, 2018, 325, pp. 31–47.
    27. 27)
      • 10. Ding, L., Han, Q.L., Guo, G.: ‘Network-based leader-following consensus for distributed multi-agent systems’, Automatica, 2013, 49, (7), pp. 2281–2286.
    28. 28)
      • 32. Sui, X., Yang, Y., Zhang, S.: ‘Leader-following consensus of multi-agent systems with randomly varying nonlinearities and stochastic disturbances under directed switching topologies’, Physica A, 2019, 525, pp. 524–534.
    29. 29)
      • 4. Shao, J., Qin, J., Bishop, A.N., et al: ‘A novel analysis on the efficiency of hierarchy among leader-following systems’, Automatica, 2016, 73, pp. 215–222.
    30. 30)
      • 11. Tan, X., Cao, J., Li, X.: ‘Consensus of leader-following multiagent systems: a distributed event-triggered impulsive control strategy’, IEEE Trans. Cybern., 2019, 49, pp. 792–801.
    31. 31)
      • 48. Tan, C., Liu, G.P., Shi, P.: ‘Consensus of networked multi-agent systems with diverse time-varying communication delays’, J. Franklin Inst., 2015, 352, (7), pp. 2934–2950.
    32. 32)
      • 2. Couzin, I.D., Krause, J., Franks, N.R., et al: ‘Effective leadership and decision-making in animal groups on the move’, Nature, 2005, 433, (7025), pp. 513–516.
    33. 33)
      • 29. Xu, X., Chen, S., Gao, L.: ‘Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design’, Neurocomputing, 2015, 156, pp. 297–305.
    34. 34)
      • 8. Guo, W.: ‘Leader-following consensus of the second-order multi-agent systems under directed topology’, ISA Trans., 2016, 65, pp. 116–124.
    35. 35)
      • 20. Xie, D., Cheng, Y.: ‘Bounded consensus tracking for sampled-data second-order multi-agent systems with fixed and markovian switching topology’, Int. J. Robust Nonlinear Control, 2015, 25, (2), pp. 252–268.
    36. 36)
      • 22. Cai, H., Huang, J.: ‘Leader-following consensus of multiple uncertain Euler-Lagrange systems under switching network topology’, Int. J. Gen. Syst., 2014, 43, (3-4), pp. 294–304.
    37. 37)
      • 36. Zhu, Y., Zheng, W.X.: ‘Multiple Lyapunov functions analysis approach for discrete-time-switched piecewise-affine systems under dwell-time constraints’, IEEE Trans. Autom. Control, 2020, 65, (5), pp. 2177–2184.
    38. 38)
      • 15. Hua, C., Li, Z., Li, K., et al: ‘Event-based leader-following consensus for uncertain non-linear multiagent systems’, IET Control Theory Appl., 2020, 14, pp. 577–583.
    39. 39)
      • 3. Nagy, M., Ákos, Z., Biro, D., et al: ‘Hierarchical group dynamics in pigeon flocks’, Nature, 2010, 464, (7290), pp. 890–893.
    40. 40)
      • 45. You, X., Hua, C., Peng, D., et al: ‘Leader-following consensus for multi-agent systems subject to actuator saturation with switching topologies and time-varying delays’, IET Control Theory Appl., 2016, 10, (2), pp. 144–150.
    41. 41)
      • 23. Su, Y., Huang, J.: ‘Two consensus problems for discrete-time multi-agent systems with switching network topology’, Automatica, 2012, 48, (9), pp. 1988–1997.
    42. 42)
      • 16. Wei, C., Luo, J., Yin, Z., et al: ‘Leader-following consensus of second-order multi-agent systems with arbitrarily appointed-time prescribed performance’, IET Control Theory Appl., 2018, 12, (16), pp. 2276–2286.
    43. 43)
      • 41. Zhu, W., Cheng, D.: ‘Leader-following consensus of second-order agents with multiple time-varying delays’, Automatica, 2010, 46, (12), pp. 1994–1999.
    44. 44)
      • 21. Xu, G.H., Guan, Z.H., He, D.X., et al: ‘Distributed tracking control of second-order multi-agent systems with sampled data’, J. Franklin Inst., 2014, 351, (10), pp. 4786–4801.
    45. 45)
      • 35. Zhu, Y., Zheng, W.X., Zhou, D.: ‘Quasi-synchronization of discrete-time Lur'e-type switched systems with parameter mismatches and relaxed PDT constraints’, IEEE Trans. Cybern., 2020, 50, (5), pp. 2026–2037.
    46. 46)
      • 46. Xue, D., Yao, J., Wang, J., et al: ‘Formation control of multi-agent systems with stochastic switching topology and time-varying communication delays’, IET Control Theory Appl., 2013, 7, (13), pp. 1689–1698.
    47. 47)
      • 9. Hu, J., Feng, G.: ‘Distributed tracking control of leader-follower multi-agent systems under noisy measurement’, Automatica, 2010, 46, (8), pp. 1382–1387.
    48. 48)
      • 18. Ji, F., Li, Y., Xiang, J.: ‘Synchronized output regulation of leader-following heterogeneous networked systems via repetitive controllers’, ISA Trans., 2017, 71, pp. 138–147.
    49. 49)
      • 43. Ding, L., Guo, G.: ‘Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay’, J. Franklin Inst., 2015, 352, (1), pp. 369–383.
    50. 50)
      • 34. Zhu, Y., Zheng, W.X.: ‘Observer-based control for cyber-physical systems with periodic doS attacks via a cyclic switching strategy’, IEEE Trans. Autom. Control, 2020, 65, (8), pp. 3714–3721.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2020.0892
Loading

Related content

content/journals/10.1049/iet-cta.2020.0892
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading