access icon free Distributed adaptive consensus tracking control for non-linear multi-agent systems with time-varying delays

In this study, a novel distributed adaptive controller is provided for consensus control of high-order non-linear multi-agent systems with unknown time-varying delays. The system is subject to uncertain disturbances, and the agents' dynamics are not known. Unlike the existing literature, the proposed method does not require time-delay terms in system dynamics to be bounded. A neural network is used to model the unknown non-linear dynamics. Then, despite the destabilising effect of the unknown delays, some adaptive rules based on the dynamic surface control are designed to achieve the consensus objective. The semi-global uniform boundedness of the resultant closed-loop signals and the convergence of the tracking errors to a neighbourhood of the origin are shown mathematically. Simulations verify the effectiveness of the results.

Inspec keywords: control system synthesis; nonlinear control systems; uncertain systems; neurocontrollers; Lyapunov methods; distributed control; multi-robot systems; delays; time-varying systems; adaptive control; closed loop systems; multi-agent systems

Other keywords: time-delay terms; consensus control; adaptive controller; consensus objective; high-order nonlinear multiagent systems; uncertain disturbances; agents; dynamic surface control; adaptive rules; nonlinear dynamics; unknown delays; unknown time-varying delays; distributed adaptive consensus tracking control; system dynamics

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Self-adjusting control systems; Stability in control theory; Multivariable control systems

References

    1. 1)
      • 25. Chang, Y.H., Chan, W.S., Wu, C.I.: ‘Distributed adaptive dynamic surface containment control for uncertain multiple euler–lagrange systems’, Int. J. Control Autom. Syst., 2018, 16, (2), pp. 403416.
    2. 2)
      • 31. Petrillo, A., Salvi, A., Santini, S., et al: ‘Adaptive synchronization of linear multi-agent systems with time-varying multiple delays’, J. Franklin Inst., 2017, 354, (18), pp. 85868605.
    3. 3)
      • 15. Jiang, X., Xia, G., Feng, Z.: ‘Output consensus of high-order linear multi-agent systems with time-varying delays’, IET Control Theory Appl., 2009, 13, (8), pp. 10841094.
    4. 4)
      • 29. Hashemi, M., Askari, J., Ghaisari, J., et al: ‘Adaptive compensation for actuator failure in a class of non-linear time-delay systems’, IET Control Theory Appl., 2015, 9, (5), pp. 710722.
    5. 5)
      • 22. Wanga, W., Wenb, C., Huang, J.: ‘Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances’, Automatica, 2017, 77, pp. 133142.
    6. 6)
      • 11. Yuanqing, W., Renquan, L., Peng, S., et al: ‘Adaptive output synchronization of heterogeneous network with an uncertain leader’, Automatica, 2017, 76, pp. 183192.
    7. 7)
      • 10. Zhen Feng, Y., Xing Zheng, W.: ‘Group consensus control for discrete-time heterogeneous first- and second-order multi-agent systems’, IET Control Theory Appl., 2018, 12, (6), pp. 753760.
    8. 8)
      • 28. Lin, P., Jia, Y.: ‘Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies’, IEEE Trans. Autom. Control, 2010, 55, (3), pp. 778784.
    9. 9)
      • 35. Chen, K., Wang, J., Zhang, Y., et al: ‘Leader-following consensus for a class of nonlinear strick-feedback multiagent systems with state time-delays’, IEEE Trans. Syst. Man Cybern., 2020, 50, pp. 23512361, doi: 10.1109/TSMC.2018.2813399.
    10. 10)
      • 32. Fiengo, G., Lui, D.G., Petrillo, A., et al: ‘Distributed leader-tracking adaptive control for high-order nonlinear lipschitz multi-agent systems with multiple time-varying communication delays’, Int. J. Control, 2019, pp. 113, doi: 10.1080/00207179.2019.1683608.
    11. 11)
      • 21. Liu, Y-J., Zeng, Q., Tong, S., et al: ‘Actuator failure compensation-based adaptive control of active suspension systems with prescribed performance’, IEEE Trans. Ind. Electron., 2020, 67, (8), pp. 70447053.
    12. 12)
      • 37. Cheng, L., Hou, Z., Tan, M., et al: ‘Neural-network-Based adaptive leader-following control for multiagent systems with uncertainties’, IEEE Trans. Neural Netw., 2010, 21, (8), pp. 13511358.
    13. 13)
      • 24. Yoo, S.J.: ‘Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (4), pp. 666672.
    14. 14)
      • 36. Ma, H., Wang, Z., Wang, D., et al: ‘Neural-network-Based distributed adaptive robust control for a class of nonlinear multiagent systems with time delays and external noises’, IEEE Trans. Syst. Man, Cybern., 2016, 46, (6), pp. 750758.
    15. 15)
      • 3. Yu, W., Chen, G., Wang, Z., et al: ‘Distributed consensus filtering in sensor networks’, IEEE Trans. Syst., Man, Cybern., B, Cybern., 2009, 39, (6), pp. 15681577.
    16. 16)
      • 1. Ogren, P., Fiorelli, E., Leonard, N.E.: ‘Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment’, IEEE Trans. Autom. Control, 2004, 49, (8), pp. 12921302.
    17. 17)
      • 40. Ge, S., Hong, F., Lee, T.H.: ‘Robust adaptive control of nonlinear systems with unknown time delays’, Automatica, 2005, 41, (7), pp. 11811190.
    18. 18)
      • 41. Das, A., Lewis, F.L.: ‘Distributed adaptive control for synchronization of unknown nonlinear networked systems’, Automatica, 2010, 46, (12), pp. 20142021.
    19. 19)
      • 19. Shen, Q., Shi, P.: ‘Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form’, Automatica, 2015, 53, pp. 120124.
    20. 20)
      • 30. Fiengo, G., Lui, D.G., Petrillo, A., et al: ‘Distributed robust output consensus for linear multi-agent systems with input time-varying delays and parameter uncertainties’, IET Control Theory Appl., 2018, 13, (2), pp. 203212.
    21. 21)
      • 8. Ghasemi, A., Askari, J., Menhaj, M.B.: ‘Distributed fault detection and isolation of actuator faults in multi-agent systems with complex-weights directed communication topology’, J. Control, Autom. Electr. Syst., 2018, 29, (6), pp. 692702.
    22. 22)
      • 23. Lu, K., Liu, Z., Lai, G., et al: ‘Adaptive consensus tracking control of uncertain nonlinear multiagent systems with predefined accuracy’, IEEE Trans. Cybern., 2019, 51, pp. 405415, doi:10.1109/TCYB.2019.2933436.
    23. 23)
      • 17. Zhang, X., Chen, M., Wang, L.: ‘Distributed event-triggered consensus in multi-agent systems with non-linear protocols’, IET Control Theory Appl., 2015, 9, (18), pp. 26262633.
    24. 24)
      • 14. Seo, J.H., Shim, H., Back, J.: ‘Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach’, Automatica, 2009, 45, (11), pp. 26592664.
    25. 25)
      • 42. Hardy, G.H., Littlewood, J.E., Polya, G.: ‘Inequalities’ (Cambridge University Press, Cambridge, MA, 1952).
    26. 26)
      • 16. Wang, L., Feng, W., Chen, M., et al: ‘Consensus of nonlinear multi-agent systems with adaptive protocols’, IET Control Theory Appl., 2014, 8, (18), pp. 22452252.
    27. 27)
      • 4. Bidram, A., Davoudi, A., Lewis, F., et al: ‘Distributed adaptive voltage control of inverter-based microgrids’, IEEE Trans. Energy Convers., 2014, 29, (4), pp. 862872.
    28. 28)
      • 6. Luo, X., Liu, D., Guan, X., et al: ‘Flocking in target pursuit for multi-agent systems with partial informed agents’, IET Control Theory Appl., 2012, 6, (4), pp. 560569.
    29. 29)
      • 26. Zhang, S., Tang, Z., Ge, S.S., et al: ‘Adaptive neural dynamic surface control of output constrained non-linear systems with unknown control direction’, IET Control Theory Appl., 2017, 11, (17), pp. 29943003.
    30. 30)
      • 34. Philip Chen, C.L., Wen, G.X., Liu, Y.J., et al: ‘Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (6), pp. 12171226.
    31. 31)
      • 43. Swaroop, D., Hedrick, J.K., Yip, P.P., et al: ‘Dynamic surface control for a class of nonlinear systems’, IEEE Trans. Autom. Control, 2000, 45, (10), pp. 18931899.
    32. 32)
      • 13. Ma, C-Q., Zhang, J-F.: ‘Necessary and sufcient conditions for consensusability of linear multi-agent systems’, IEEE Trans. Autom. Control, 2010, 55, (5), pp. 12631268.
    33. 33)
      • 27. Zhang, Z., Duan, G., Hou, M.: ‘Robust adaptive dynamic surface control of uncertain non-linear systems with output constraints’, IET Control Theory Appl., 2016, 11, (1), pp. 110121.
    34. 34)
      • 7. Zou, Y., Wen, C., Guan, M.: ‘Distributed adaptive control for distance-based formation and flocking control of multi-agent systems’, IET Control Theory Appl., 2019, 13, (6), pp. 878885.
    35. 35)
      • 9. Shahvali, M., Bagher Naghibi-Sistani, M., Askari, J.: ‘Adaptive output feedback bipartite consensus for nonstrict-feedback nonlinear multi-agent systems: a finite-time approach’, Neurocomputing, 2018, 318, (6), pp. 717.
    36. 36)
      • 45. Zamani, N., Askari, J., Kamali, M.: ‘A simple distributed adaptive consensus tracking control of high order nonlinear multi-agent systems’. Proc. 27nd Iranian Conf. Electrical Engineering (ICEE), Iran, 2019, pp. 10751080.
    37. 37)
      • 44. Wu, M., He, Y., She, J., et al: ‘Delay-dependent criteria for robust stability of time-varyingdelay systems’, Automatica, 2004, 40, pp. 14351439.
    38. 38)
      • 5. Liu, L., Liu, Y-J., Li, D., et al: ‘Barrier Lyapunov function-based adaptive fuzzy FTC for switched systems and its applications to resistance-inductance-capacitance circuit system’, IEEE Trans. Cybern., 2020, 50, pp. 34913502, doi:10.1109/TCYB.2019.2931770.
    39. 39)
      • 18. Shi, C., Yang, G., Li, X.: ‘Robust adaptive backstepping control for hierarchical multi-agent systems with signed weights and system uncertainties’, IET Control Theory Appl., 2017, 11, (16), pp. 27432752.
    40. 40)
      • 38. Zuo, Z., Wang, C.: ‘Adaptive trajectory tracking control of output constrained multi-rotors systems’, IET Control Theory Appl., 2014, 8, (13), pp. 11631174.
    41. 41)
      • 20. Tang, L., Li, D.: ‘Time-varying barrier Lyapunov function based adaptive neural controller design for nonlinear pure-feedback systems with unknown hysteresis’, Int. J. Control Autom. Syst., 2019, 17, (7), pp. 16421654.
    42. 42)
      • 2. Du, J., Guo, C., Yu, S., et al: ‘Adaptive autopilot design of time varying uncertain ships with completely unknown control coefficient’, IEEE J. Ocean Eng., 2007, 32, (2), pp. 346352.
    43. 43)
      • 12. Tuna, S.E.: ‘Conditions for synchronizability in arrays of coupled linear systems’, IEEE Trans. Autom. Control, 2009, 54, (10), pp. 24162420.
    44. 44)
      • 33. Zhanga, H., Lewis, F.: ‘Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics’, Automatica, 2012, 48, (7), pp. 14321439.
    45. 45)
      • 39. Ren, W., Cao, Y.: ‘Distributed coordination of multi-agent networks: emergent problems, models and issues’ (Springer-Verlag, London, 2010).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2020.0281
Loading

Related content

content/journals/10.1049/iet-cta.2020.0281
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading