Robust cooperative control for micro/nano scale systems subject to time-varying delay and structured uncertainties

  • Yanzhou Li
  • Yongkang LuEmail author
  • Yuanqing Wu
  • Shenghuang He


In this study, a robust cooperative control methodology is proposed for a class of micro/nano scale systems in the field of biomedical engineering. Due to the complexity of actual environment, the dynamic behavior of the micro/nano scale systems changes over time. The time-varying uncertainties are considered to be restricted to a certain range. Then, a robust cooperative control strategy is designed such that the micro-agents with structured uncertainties can securely cooperative with each other to accomplish the tasks. Furthermore, sufficient conditions ensuring the cooperativity of micro/nano scale systems are derived by constructing a novel Lyapunov functional. It is proved that the cooperative control problem for micro/nano scale systems can be solved if the control parameters are appropriately selected. A simulation example is presented to demonstrate the validity of the obtained algorithm.


Micro/nano scale systems Robust cooperative control Uncertainties 



This work was partially supported by National Key R&D Program of China (2018YFB1700400), the Innovative Research Team Program of Guangdong Province Science Foundation (2018B030312006), the Fundamental Research Funds for the Central Universities (2017FZA5010), the Science and Technology Planning Project of Guangdong Province (2017B010116006).


  1. 1.
    Becker A, Onyuksel C, Bretl T, Mclurkin J (2014) Controlling many differential-drive robots with uniform control inputs. Int J Robot Res 33(13):1626–1644CrossRefGoogle Scholar
  2. 2.
    Ge X, Han QL, Ding D, Zhang XM, Ning B (2018) A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems. Neurocomputing 275(31):1684–1701CrossRefGoogle Scholar
  3. 3.
    Song G, Rui S, Li Y (2018) Cooperative control of multiple nonholonomic robots for escorting and patrolling mission based on vector field. IEEE Access 6:41883–41891CrossRefGoogle Scholar
  4. 4.
    Wang Q, Psillakis HE, Sun C (2018) Cooperative control of multiple agents with unknown high-frequency gain signs under unbalanced and switching topologies. IEEE Transactions on Automatic Control. MathSciNetCrossRefGoogle Scholar
  5. 5.
    Meng Y, Chen Q, Rahmani A (2018) A decentralized cooperative control scheme for a distributed space transportation system. Robot Autonom Syst 101(3):1–19CrossRefGoogle Scholar
  6. 6.
    Brandao AS, Barbosa JPA, Mendoza V, Sarcinelli-Filho M, Carelli R (2014) A multi-layer control scheme for a centralized UAV formation. International Conference on Unmanned Aircraft SystemsGoogle Scholar
  7. 7.
    Zhuo Z, Yang S, Zhang Z, Hui Z, Sheng B (2018) Modified order-reduction method for distributed control of multi-spacecraft networks with time-varying delays. IEEE Trans Control Netw Syst 5(1):79–92MathSciNetCrossRefGoogle Scholar
  8. 8.
    Tucci M, Riverso S, Vasquez JC, Guerrero JM, Ferrari-Trecate G (2016) A decentralized scalable approach to voltage control of DC islanded microgrids. IEEE Trans Control Syst Technol 26(4):1965–1979CrossRefGoogle Scholar
  9. 9.
    Zhao D, Ding SX, Karimi HR, Li Y, Wang Y (2019) On robust Kalman filter for two-dimension uncertain linear discrete time-varying systems: a least squares method. Automatica 99:203–212MathSciNetCrossRefGoogle Scholar
  10. 10.
    Zhao D, Ding SX, Wang Y, Li Y (2018) Krein-space based robust H fault estimation for two-dimensional uncertain linear discrete time-varying systems. Syst Control Lett 115:41–47MathSciNetCrossRefGoogle Scholar
  11. 11.
    Li S, Er MJ, Zhang J (2018) Distributed adaptive fuzzy control for output consensus of heterogeneous stochastic nonlinear multiagent systems. IEEE Trans Fuzzy Syst 26(3):1138–1152Google Scholar
  12. 12.
    Li Z, Wen G, Duan Z, Ren W (2015) Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs. IEEE Trans Autom Control 60(4):1152–1157MathSciNetCrossRefGoogle Scholar
  13. 13.
    Qiu Z, Liu S, Xie L (2016) Distributed constrained optimal consensus of multi-agent systems. Automatica 68:209–215MathSciNetCrossRefGoogle Scholar
  14. 14.
    Wu Y, Karimi HR, Lu R (2018) Sampled-data control of network systems in industrial manufacturing. IEEE Trans Indus Electron 65(11):9016–9024CrossRefGoogle Scholar
  15. 15.
    Wang Y, Tan KT, Peng XY, So PL (2016) Coordinated control of distributed energy-storage systems for voltage regulation in distribution networks. IEEE Trans Power Delivery 31(3):1132–1141CrossRefGoogle Scholar
  16. 16.
    Liu Y, Wang Z, Liang J, Liu X (2008) Robust H control of a class sample-data system for satellite attitude control with structured uncertainty. Aerospace ControlGoogle Scholar
  17. 17.
    Kazemy A (2017) Robust mixed H /passive vibration control of offshore steel jacket platforms with structured uncertainty. Ocean Eng 139(5):95–102CrossRefGoogle Scholar
  18. 18.
    Zhao D, Wang Y, Li Y, Ding SX (2018) H fault estimation for two-dimensional linear time-varying systems based on Krein space method. Int J Control 48 (12):2070–2079Google Scholar
  19. 19.
    Wang Y, Yang X, Yan H (2019) Reliable fuzzy tracking control of near-space hypersonic vehicle using aperiodic measurement information. IEEE Transactions on Industrial Electronics. CrossRefGoogle Scholar
  20. 20.
    Wang Y, Karimi HR, Lam HK, Shen H (2019) An improved result on exponential stabilization of sampled-data fuzzy systems. IEEE Trans Fuzzy Syst 26(6):3875–3883CrossRefGoogle Scholar
  21. 21.
    Liu Y, Wang Z, Liang J, Liu X (2008) Robust distributed model predictive control of linear systems with structured time-varying uncertainties. Int J Control 90(11):1–20MathSciNetGoogle Scholar
  22. 22.
    Patre PM, MacKunis W, Makkar C, Dixon WE (2008) Asymptotic tracking for systems with structured and unstructured uncertainties. IEEE Trans Control Syst Technol 16(2):373–397CrossRefGoogle Scholar
  23. 23.
    Perera LP, Oliveira P, Soares CG (2016) System identification of vessel steering with unstructured uncertainties by persistent excitation maneuvers. IEEE J Ocean Eng 41(3):515–528Google Scholar
  24. 24.
    Hu J, Wang Z, Gao H, Stergioulas LK (2012) Asymptotic tracking for systems with structured and unstructured uncertainties. IEEE Trans Control Syst Technol 59(7):3008–3015Google Scholar
  25. 25.
    Mathiyalagan K, Park JH, Sakthivel R (2015) Exponential synchronization for fractional-order chaotic systems with mixed uncertainties. Complexity 21(1):114–125MathSciNetCrossRefGoogle Scholar
  26. 26.
    Ma Q, Lu J, Xu H (2015) Consensus for nonlinear multi-agent systems with sampled data. Trans Instit Measur Control 36(5):618–626CrossRefGoogle Scholar
  27. 27.
    Lu J, Ho DW (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern Part B (Cybern) 40(2):350–361CrossRefGoogle Scholar
  28. 28.
    Xie L (1996) Output feedback H control of systems with parameter uncertainty. Int J Control 63(4):741–750MathSciNetCrossRefGoogle Scholar
  29. 29.
    Jiang B, Karimi HR, Kao Y, Gao C (2019) Reduced-order adaptive sliding mode control for nonlinear switching semi-Markovian jump delayed systems. Inf Sci 477:334–348MathSciNetCrossRefGoogle Scholar
  30. 30.
    Jiang B, Karimi HR, Kao Y, Gao C (2018) Fuzzy-model-based sliding mode control of nonlinear descriptor systems. IEEE Trans Cybern (Early Access) 477:334–348Google Scholar
  31. 31.
    Wang Y, Karimi HR, Shen H, Fang Z, Liu M (2018) A novel robust fuzzy integral sliding mode control for nonlinear semi-Markovian jump T-S fuzzy systems. IEEE Transactions on Fuzzy Systems. CrossRefGoogle Scholar
  32. 32.
    Karimi HR, Jabedar Maralani P, Lohmann B, Moshiri B (2005) H control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions. Int J Control 78(4):254–263MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Yanzhou Li
    • 1
  • Yongkang Lu
    • 1
    Email author
  • Yuanqing Wu
    • 1
  • Shenghuang He
    • 1
  1. 1.Guangdong Province Key Laboratory of Intelligent Decision and Cooperative ControlGuangzhouChina

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