Consensus for non-linear multi-agent systems modelled by PDEs based on spatial boundary communication

Consensus for non-linear multi-agent systems modelled by PDEs based on spatial boundary communication

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

There is spatio-temporal nature for many multi-agent systems such as infight hose-and-drogue aerial refuelling systems. To deal with consensus control of such cases, this study establishes a non-linear leader-following spatio-temporal multi-agent system modelled by partial differential equations. Initially, a boundary controller based on boundary coupling is studied to ensure consensus of the multi-agent system. A sufficient condition on the existence of the controller for consensus is presented in terms of linear matrix inequalities. To simplify the obtained result, a second boundary controller is studied and a simple sufficient condition of its existence is investigated. Finally, two numerical examples demonstrate the effectiveness of the proposed methods. The merits of the proposed controllers lie in making use of only spatial boundary communication and requiring actuators and sensors only at spatial boundary positions.


    1. 1)
      • 1. Cui, G., Xu, S., Lewis, F.L., et al.: ‘Distributed consensus tracking for non-linear multi-agent systems with input saturation: a command filtered backstepping approach’, IET Control Theory Appl., 2016, 10, pp. 509516.
    2. 2)
      • 2. Li, G., Wang, X., Li, S.: ‘Distributed composite output consensus protocols of higher-order multi-agent systems subject to mismatched disturbances’, IET Control Theory Appl., 2017, 11, pp. 11621172.
    3. 3)
      • 3. Li, W., Chen, Z., Liu, Z.: ‘Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics’, Nonlinear Dyn., 2013, 72, pp. 803812.
    4. 4)
      • 4. Li, L., Ho, D.W., Lu, J.: ‘A consensus recovery approach to nonlinear multi-agent system under node failure’, Inf. Sci., 2016, 367, pp. 975989.
    5. 5)
      • 5. Xu, W., Cao, J., Yu, W., et al.: ‘Leader-following consensus of nonlinear multi-agent systems with jointly connected topology’, IET Control Theory Appl., 2014, 8, pp. 432440.
    6. 6)
      • 6. Wu, X., Zhu, C., Kan, H.: ‘An improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system’, Appl. Math. Comput., 2015, 252, pp. 201214.
    7. 7)
      • 7. Qin, J., Yu, C.: ‘Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition’, Automatica, 2013, 49, pp. 28982905.
    8. 8)
      • 8. Chen, C.P., Wen, G., Liu, Y., 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, pp. 12171226.
    9. 9)
      • 9. Xu, W., Ho, D.W.C., Li, L., et al.: ‘Event-triggered schemes on leader-following consensus of general linear multi-agent systems under different topologies’, IEEE Trans. Cybern., 2017, 47, pp. 212223.
    10. 10)
      • 10. Chen, X., Hao, F.: ‘Event-triggered average consensus control for discrete-time multi-agent systems’, IET Control Theory Appl., 2012, 6, pp. 24932498.
    11. 11)
      • 11. Xu, X., Gao, L.: ‘Intermittent observer-based consensus control for multi-agent systems with switching topologies’, Int. J. Syst. Sci., 2016, 47, pp. 18911904.
    12. 12)
      • 12. 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.
    13. 13)
      • 13. Song, Q., Liu, F., Cao, J., et al.: ‘M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics’, IEEE Trans. Cybern., 2013, 43, pp. 16881697.
    14. 14)
      • 14. He, W., Chen, G., Han, Q.L., et al.: ‘Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control’, Inf. Sci., 2015, 380, pp. 145158.
    15. 15)
      • 15. Zhao, Y., Duan, Z., Wen, G.: ‘Finite-time consensus for second-order multi-agent systems with saturated control protocols’, IET Control Theory Appl., 2015, 9, pp. 312319.
    16. 16)
      • 16. Zhao, L., Jia, Y., Yu, J., et al.: ‘H sliding mode based scaled consensus control for linear multi-agent systems with disturbances’, Appl. Math. Comput., 2017, 292, pp. 375389.
    17. 17)
      • 17. Wang, J., Wu, H., Li, H.: ‘Guaranteed cost distributed fuzzy observer-based control for a class of nonlinear spatially distributed processes’, AIChE J., 2013, 59, pp. 23662378.
    18. 18)
      • 18. Sheng, L., Yang, H., Lou, X.: ‘Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms', Chaos Solitons Fractals, 2009, 40, pp. 930939.
    19. 19)
      • 19. Yu, F., Jiang, H.: ‘Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms’, Neurocomputing, 2011, 74, pp. 509515.
    20. 20)
      • 20. Yang, C., Qiu, J., He, H.: ‘Exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients’, Neurocomputing, 2015, 151, pp. 4047.
    21. 21)
      • 21. Hu, C., Jiang, H., Teng, Z.: ‘Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms’, IEEE Trans. Neural Netw., 2010, 21, pp. 6781.
    22. 22)
      • 22. Hu, C., Yu, J., Jiang, H., et al.: ‘Exponential synchronization for reaction-diffusion networks with mixed delays in terms of p-norm via intermittent driving’, Neural Netw., 2012, 31, pp. 111.
    23. 23)
      • 23. Gan, Q.: ‘Adaptive synchronization of stochastic neural networks with mixed time delays and reaction-diffusion terms’, Nonlinear Dyn., 2012, 69, pp. 22072219.
    24. 24)
      • 24. Wang, J., Wu, H.: ‘Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling’, IEEE Trans. Cybern., 2014, 44, pp. 13501361.
    25. 25)
      • 25. Wang, J., Wu, H., Guo, L.: ‘Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, pp. 429440.
    26. 26)
      • 26. Wang, J., Yang, C., Sun, C.: ‘Exponential synchronization for a class of networked linear parabolic PDE systems via boundary control’. Proc. 2014 Int. Joint Conf. Neural Networks, Beijing, China, July 2014, pp. 39813986.
    27. 27)
      • 27. Wu, K., Tian, T., Wang, L.: ‘Synchronization for a class of coupled linear partial differential systems via boundary control’, J. Franklin Inst., 2016, 353, pp. 40624073.
    28. 28)
      • 28. Wu, K., Tian, T., Wang, L., et al.: ‘Asymptotical synchronization for a class of coupled time-delay partial differential systems via boundary control’, Neurocomputing, 2016, 197, pp. 113118.
    29. 29)
      • 29. Yang, C., Cao, J., Huang, T., et al.: ‘‘Guaranteed cost boundary control for cluster synchronization of complex spatio-temporal dynamical networks with community structure’, Sci. China Inf. Sci., 2017, doi:10.1007/s11432-016-9099-x.
    30. 30)
      • 30. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, pp. 28602866.
    31. 31)
      • 31. Song, Q., Cao, J.: ‘On pinning synchronization of directed and undirected complex dynamical networks’, IEEE Trans. Circuits Syst. I, 2010, 57, pp. 672680.
    32. 32)
      • 32. Guo, Z., Yang, S., Wang, J.: ‘Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control’, Neural Netw., 2016, 84, pp. 6779.
    33. 33)
      • 33. Ai, Z., Zong, G.: ‘Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems’, Appl. Math. Comput., 2014, 245, pp. 462473.
    34. 34)
      • 34. Huang, T., Li, C., Yu, W., et al.: ‘Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback’, Nonlinearity, 2009, 22, pp. 569584.
    35. 35)
      • 35. Huang, T., Li, C., Duan, S., et al.: ‘Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 23, pp. 866875.
    36. 36)
      • 36. Wu, H., Wang, J., Li, H.: ‘Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems’, IEEE Trans. Fuzzy Syst., 2014, 22, pp. 642652.
    37. 37)
      • 37. Wang, J., Wu, H., Sun, C.: ‘Boundary controller design and well-posedness analysis of semi-linear parabolic PDE systems’. Proc. 2014 American Control Conf., Portland, Oregon, USA, July 2014, pp. 33693374.
    38. 38)
      • 38. Demetriou, M.A.: ‘Design of consensus and adaptive consensus filters for distributed parameter systems’, Automatica, 2010, 46, pp. 300311.

Related content

This is a required field
Please enter a valid email address