Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free leader-based consensus of non-linear multi-agents over switching graphs and disturbances using multiple Lyapunov functions

© The Institution of Engineering and Technology
Received 29/03/2020, Accepted 28/09/2020, Revised 26/07/2020, Published 03/12/2020

This study deals with the multiple Lyapunov functions approach for the robust leader-following consensus of one-sided Lipschitz (OSL) multiagents, connected via switching topologies under external disturbances. Disturbances have been accounted for followers, connected via a directed graph with a spanning tree from the leader root. The authors stipulate two consensus protocols, based on the absence or existence of norm-bounded reference input to the leader, and provide matrix inequalities for designing the parameters of consensus controllers. In the presence of bounded disturbances, the proposed protocol ensures consensus criterion for minimisation of the effect of disturbances to the consensus error between the leader and followers. A remedy for striking robustness against external perturbations has been provided in the present work in contrast to the conventional consensus schemes on OSL agents. Switching OSL mobile agents and aircraft carriers consisting of a leader and five followers have been simulated in the existence of reference input and disturbances to demonstrate the empirical proficiency of the consensus protocol schemes.

Inspec keywords: directed graphs; distributed control; robust control; linear systems; uncertain systems; linear matrix inequalities; multi-agent systems; control system synthesis; Lyapunov methods

Other keywords: multiple Lyapunov functions approach; consensus protocols; nonlinear multiagents; directed graph; external perturbations; consensus error; consensus controllers; norm-bounded reference input; one-sided Lipschitz multiagents; matrix inequalities; leader root; spanning tree; striking robustness; OSL mobile agents; consensus protocol schemes; robust leader; external disturbances; H∞ consensus criterion

Subjects: Linear control systems; Control system analysis and synthesis methods; Combinatorial mathematics; Linear algebra (numerical analysis); Multivariable control systems; Stability in control theory

References

    1. 1)
      • 16. Agha, R., Rehan, M., Ahn, C. K., et al: ‘Adaptive distributed consensus control of one-sided lipschitz nonlinear multiagents’, IEEE Trans. Syst. Man Cyber. Syst., 2019, 49, (3), pp. 568–578.
    2. 2)
      • 46. Li, Z., Liu, X., Ren, W., et al: ‘Distributed tracking control for linear multiagent systems with leader of bounded unknown input’, IEEE Trans. Autom. Control, 2013, 58, (2), pp. 518–523.
    3. 3)
      • 23. Li, Z., Liu, X., Fu, M., et al: ‘Global H∞ consensus of multi-agent systems with lipschitz non-linear dynamics’, IET Control Theory Appl., 2012, 6, (13), pp. 2041–2048.
    4. 4)
      • 28. Wen, G., Hu, G., Yu, W., et al: ‘Distributed H∞ consensus of higher order multiagent systems with switching topologies’, IEEE Trans. Circuits Syst. II, Express Briefs, 2014, 61, (5), pp. 359–363.
    5. 5)
      • 9. Abbaszadeh, M., Marquez, H.J.: ‘Nonlinear observer design for one-sided lipschitz systems’. Proc. American Control Conf., Baltimore, USA, 2010, pp. 5284–5289.
    6. 6)
      • 34. Hua, Y., Dong, X., Li, Q.: ‘Distributed time-varying formation robust tracking for general linear multiagent systems with parameter uncertainties and external disturbances’, IEEE Trans. Cybern., 2017, 47, (8), pp. 1959–1969.
    7. 7)
      • 15. Wen, G., Yu, W., Xia, Y., et al: ‘Distributed tracking of nonlinear multiagent systems under directed switching topology: an observer-based protocol’, IEEE Trans. Syst., Man Cyber. Syst., 2017, 47, (5), pp. 869–881.
    8. 8)
      • 19. Wen, G., Zheng, W. X.: ‘On constructing multiple lyapunov functions for tracking control of multiple agents with switching topolgies’, IEEE Trans. Autom. Control, 2019, 64, (9), pp. 3796–3803.
    9. 9)
      • 7. Rehan, M., Jameel, A., Ahn, C. K.: ‘Distributed consensus control of one-sided lipschitz nonlinear multiagent systems’, IEEE Trans. Syst., Man Cybern. Syst., 2018, 48, (8), pp. 1297–1308.
    10. 10)
      • 32. Wang, X., Yang, G.: ‘Distributed H∞ consensus tracking control for multi-agent networks with switching directed topologies’, Neurocomputing, 2016, 207, pp. 693–699.
    11. 11)
      • 13. 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, 2019, 325, pp. 37–47.
    12. 12)
      • 40. Chadli, M., Davoodi, M., Meskin, N.: ‘Distributed state estimation, fault detection and isolation filter design for heterogeneous multi-agent linear parameter-varying systems’, IET Control Theory Appl., 2017, 11, (2), pp. 254–262.
    13. 13)
      • 22. Lin, P., Jia, Y., Li, L.: ‘Distributed robust H∞ consensus control in directed networks of agents with time-delay’, Syst. Control Lett., 2008, 57, (8), pp. 643–653.
    14. 14)
      • 10. Ahmad, S., Rehan, M.: ‘On observer-based control of one-sided lipschitz systems’, J. Franklin Inst., 2016, 353, (4), pp. 903–916.
    15. 15)
      • 29. Guo, X., Wang, J., Liao, F., et al: ‘Quantized H∞ consensus of multiagent systems with quantization mismatch under switching weighted topologies’, IEEE Trans. Control Netw. Syst., 2017, 4, (2), pp. 202–212.
    16. 16)
    17. 17)
      • 39. Xu, W., Huang, Y., Zhou, X.: ‘Consensus seeking for heterogeneous networks of agents with non-convex constraints and switching topologies’, IET Control Theory Appl., 2020, 14, (6), pp. 809–815.
    18. 18)
      • 25. Dong, X., Xi, J., Shi, Z., et al: ‘Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances’, Int. J. Syst. Sci., 2013, 44, (10), pp. 1843–1856.
    19. 19)
    20. 20)
    21. 21)
      • 47. Nguyen, C.-M., Pathirana, P.-N., Trinh, H.: ‘Robust observer and observer-based control designs for discrete one-sided lipschitz systems subject to uncertainties and disturbances’, Appl. Math. Comput., 2019, 353, pp. 42–53.
    22. 22)
    23. 23)
    24. 24)
      • 21. Cao, Y., Zhang, L., Li, C., et al: ‘Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology’, IEEE Trans. Cybern., 2017, 47, (8), pp. 2212–2222.
    25. 25)
      • 41. Gong, P., Wang, K.: ‘Output feedback consensus control for fractional-order nonlinear multi-agent systems with directed topologies’, J. Franklin Inst., 2020, 357, (3), pp. 1473–1493.
    26. 26)
      • 24. Zhao, Y., Duan, Z., Wen, G., et al: ‘Distributed H∞ consensus of multi-agent systems: a performance region-based approach’, Int. J. Control, 2012, 85, (3), pp. 332–341.
    27. 27)
      • 27. Saboori, I., Khorasani, K.: ‘ H∞ consensus achievement of multi-agent systems with directed and switching topology networks’, IEEE Trans. Autom. Control, 2014, 59, (11), pp. 3104–3109.
    28. 28)
      • 45. Xu, Y., Fang, M., Wu, Z., et al: ‘Input-based event-triggering consensus of multiagent systems under denial-of-service attacks’, IEEE Trans. System, Man Cybern. Syst., 2020, 50, (4), pp. 1455–1464.
    29. 29)
      • 43. Zou, W., Xiang, Z.: ‘Event-triggered leader–following consensus of non-linear multi-agent systems with switched dynamics’, IET Control Theory Appl., 2019, 13, (9), pp. 1222–1228.
    30. 30)
      • 3. Ren, W., Beard, R. W., Atkins, E. M.: ‘A survey of consensus problems in multi-agent coordination’. Proceed. American Control Conf., Portland, OR, USA, 2005, 3, pp. 1859–1864.
    31. 31)
      • 2. Li, Z., Duan, Z.: ‘Cooperative control of multi-agent systems: a consensus region approach’ (CRC Press, Taylor & Francis Group, Boca Raton, 2015).
    32. 32)
    33. 33)
      • 31. Zhao, Y., Duan, Z., Wen, G., et al: ‘Robust consensus tracking of multi-agent systems with uncertain lur'e-type non-linear dynamics’, IET Control Theory Appl., 2013, 7, (9), pp. 1249–1260.
    34. 34)
      • 8. Rehan, M., Ahn, C.K., Chadli, M.: ‘Consensus of one-sided lipchitz multi-agents under input saturation’, IEEE Trans. Circuits Syst. II, Express Briefs, 2020, 67, (4), pp. 745–749.
    35. 35)
      • 44. Ding, C., Dong, X., Shi, C., et al: ‘Leaderless output consensus of multi-agent systems with distinct relative degrees under switching directed topologies’, IET Control Theory Appl., 2019, 13, (3), pp. 313–320.
    36. 36)
      • 4. Olfati-Saber, R., Fax, J.A., Murray, R.M.: ‘Consensus and cooperation in networked multi-agent systems’, Proc. IEEE, 2007, 95, (1), pp. 215–233.
    37. 37)
      • 36. Liu, J., Zhang, Y., Yu, Y., et al: ‘Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications’, IEEE Trans. Syst., Man, Cybern. Syst., 2019, 49, (11), pp. 2221–2229.
    38. 38)
      • 37. Chen, Y., Wang, Z., Yuan, Y., et al: ‘Distributed H∞ filtering for switched stochastic delayed systems over sensor networks with fading measurements’, IEEE Trans. Cybern., 2020, 50, (1), pp. 2–14.
    39. 39)
      • 26. Wen, G., Duan, Z., Li, Z., et al: ‘Consensus and its L2-gain performance of multi-agent systems with intermittent information transmissions’, Int. J. Control, 2012, 85, (4), pp. 384–396.
    40. 40)
      • 33. Yu, J., Dong, X., Li, Q., et al: ‘Robust H∞ guaranteed cost time-varying formation tracking for high-order multiagent systems with time-varying delays’, IEEE Trans. Syst. Man Cybern. Syst., 2020, 50, (4), pp. 1465–1475.
    41. 41)
      • 14. Rehman, A.U., Rehan, M., Iqbal, N., et al: ‘Towards LPV approach for adaptive distributed consensus of lipschitz multi-agents’, IEEE Trans. Circuits Syst. II, Express Briefs, 2019, 66, (1), pp. 91–95.
    42. 42)
      • 12. Wang, B., Chen, W., Zhang, B.: ‘Semi-global robust tracking consensus for multi-agent uncertain systems with input saturation via metamorphic low-gain feedback’, Automatica, 2019, 103, pp. 363–373.
    43. 43)
      • 42. Xu, Z., Li, C., Han, Y.: ‘Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control’, J. Franklin Inst., 2019, 356, (1), pp. 441–456.
    44. 44)
      • 30. Wang, X., Yang, G.: ‘Distributed reliable H∞ consensus control for a class of multi-agent systems under switching networks: a topology-based average dwell time approach’, Int. J. Robust Nonlinear Control, 2016, 26, (13), pp. 2767–2787.
    45. 45)
      • 1. Cao, Y., Yu, W., Ren, W., et al: ‘An overview of recent progress in the study of distributed multi-agent coordination’, IEEE Trans. Ind. Inf., 2013, 9, (1), pp. 427–438.
    46. 46)
      • 17. Chu, H., Liu, X., Zhang, W., et al: ‘Observer-based consensus tracking of multi-agent systems with one-sided lipschitz nonlinearity’, J. Franklin Inst., 2016, 353, (7), pp. 1594–1614.
    47. 47)
      • 38. Davoodi, M., Chadli, M., Meskin, N., et al: ‘Finite frequency fault diagnosis for heterogeneous multi-agent LPV systems’. 2019 IEEE Conf. Tech. Appl. (CCTA), Hong Kong, China, 2019, pp. 1018–1023.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2020.0393
Loading

Related content

content/journals/10.1049/iet-cta.2020.0393
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address