Skip to main content
SpringerLink
Log in

Observer-based adaptive consensus control for nonlinear multi-agent systems with time-delay

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, we consider the observer-based adaptive consensus tracking problem for a class of nonlinear time-delay multi-agent systems in the presence of input saturation. Under the assumption that the communication topology is directed and connected, a distributed adaptive consensus controller is developed based on the dynamic surface control technique. By constructing the nonlinear observer, the unmeasurable agents dynamics can be estimated. Input saturation problem is solved by a smooth function combined with an auxiliary variable. With the help of prescribed performance functions, the synchronization errors converge to the prescribed sets, which are characterized as a neighborhood of zero. According to Lyapunov stability theory, it is shown that with the proposed distributed consensus tracking approach, the consensus errors are cooperatively semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to show the effectiveness of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen W S, Li X B, Ren W, et al. Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel nussbaum-type function. IEEE Trans Automat Contr, 2014, 59: 1887–1892

    Article  MathSciNet  MATH  Google Scholar 

  2. Li Z K, Ren W, Liu X D, et al. Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica, 2013, 49: 1986–1995

    Article  MathSciNet  MATH  Google Scholar 

  3. Liang H J, Zhang L C, Sun Y H, et al. Containment control of semi-Markovian multi-agent systems with switching topologies. IEEE Trans Syst Man Cybernet Syst, 2019. doi: https://doi.org/10.1109/TSMC.2019.2946248

    Google Scholar 

  4. Niu X L, Liu Y G, Li F Z. Consensus via time-varying feedback for uncertain stochastic nonlinear multiagent systems. IEEE Trans Cybern, 2019, 49: 1536–1544

    Article  Google Scholar 

  5. Zhang H P, Yue D, Zhao W, et al. Distributed optimal consensus control for multiagent systems with input delay. IEEE Trans Cybern, 2018, 48: 1747–1759

    Article  Google Scholar 

  6. Ren H R, Karimi H R, Lu R Q, et al. Synchronization of network systems via aperiodic sampled-data control with constant delay and application to unmanned ground vehicles. IEEE Trans Ind Electron, 2019. doi: https://doi.org/10.1109/TIE.2019.2928241

    Google Scholar 

  7. Lu Z H, Zhang L, Wang L. Controllability analysis of multi-agent systems with switching topology over finite fields. Sci China Inf Sci, 2019, 62: 012201

    Article  MathSciNet  Google Scholar 

  8. Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Automat Contr, 2004, 49: 1520–1533

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun H, Liu Y G, Li F Z, et al. Distributed LQR optimal protocol for leader-following consensus. IEEE Trans Cybern, 2019, 49: 3532–3546

    Article  Google Scholar 

  10. Zhu W, Zhou Q H, Wang D, et al. Fully distributed consensus of second-order multi-agent systems using adaptive event-based control. Sci China Inf Sci, 2018, 61: 129201

    Article  MathSciNet  Google Scholar 

  11. Zhang Y H, Li H Y, Sun J, et al. Cooperative adaptive event-triggered control for multiagent systems with actuator failures. IEEE Trans Syst Man Cybern Syst, 2019, 49: 1759–1768

    Article  Google Scholar 

  12. Cao L, Li H Y, Dong G W, et al. Event-triggered control for multi-agent systems with sensor faults and input saturation. IEEE Trans Syst Man Cybernet Syst, 2019. doi: https://doi.org/10.1109/TSMC.2019.2938216

    Google Scholar 

  13. Zhang Y H, Sun J, Liang H J, et al. Event-triggered adaptive tracking control for multiagent systems with unknown disturbances. IEEE Trans Cybern, 2020, 50: 890–901

    Article  Google Scholar 

  14. Wen G X, Chen C L P, Liu Y J. Formation control with obstacle avoidance for a class of stochastic multiagent systems. IEEE Trans Ind Electron, 2018, 65: 5847–5855

    Article  Google Scholar 

  15. Xu J J, Xu L, Xie L H, et al. Decentralized control for linear systems with multiple input channels. Sci China Inf Sci, 2019, 62: 052202

    Article  MathSciNet  Google Scholar 

  16. Yan X H, Liu Y G, Zheng W X. Global adaptive output-feedback stabilization for a class of uncertain nonlinear systems with unknown growth rate and unknown output function. Automatica, 2019, 104: 173–181

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen C L P, Wen G X, Liu Y J, et al. Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems. IEEE Trans Cybern, 2016, 46: 1591–1601

    Article  Google Scholar 

  18. Yu W W, Li Y, Wen G H, et al. Observer design for tracking consensus in second-order multi-agent systems: fractional order less than two. IEEE Trans Automat Contr, 2017, 62: 894–900

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen M, Shao S Y, Jiang B. Adaptive neural control of uncertain nonlinear systems using disturbance observer. IEEE Trans Cybern, 2017, 47: 3110–3123

    Article  Google Scholar 

  20. Wang H Q, Liu P X, Shi P. Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems. IEEE Trans Cybern, 2017, 47: 2568–2578

    Article  Google Scholar 

  21. Liu T, Huang J. Adaptive cooperative output regulation of discrete-time linear multi-agent systems by a distributed feedback control law. IEEE Trans Automat Contr, 2018, 63: 4383–4390

    Article  MathSciNet  MATH  Google Scholar 

  22. Li Z K, Liu X D, Lin P, et al. Consensus of linear multi-agent systems with reduced-order observer-based protocols. Syst Control Lett, 2011, 60: 510–516

    Article  MathSciNet  MATH  Google Scholar 

  23. Shi P, Shen Q K. Observer-based leader-following consensus of uncertain nonlinear multi-agent systems. Int J Robust Nonlin Control, 2017, 55: 3794–3811

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang C K, He Y, Jiang L, et al. Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality. IEEE Trans Cybern, 2017, 47: 3040–3049

    Article  Google Scholar 

  25. Lin Z L. Control design in the presence of actuator saturation: from individual systems to multi-agent systems. Sci China Inf Sci, 2019, 62: 026201

    Article  Google Scholar 

  26. Liu J W, Huang J. Leader-following consensus of linear discrete-time multi-agent systems subject to jointly connected switching networks. Sci China Inf Sci, 2018, 61: 112208

    Article  MathSciNet  Google Scholar 

  27. Wen G X, Chen C L P, Liu Y J, et al. Neural network-based adaptive leader-following consensus control for a class of nonlinear multiagent state-delay systems. IEEE Trans Cybern, 2017, 47: 2151–2160

    Article  Google Scholar 

  28. Wang W, Wang D, Peng Z, et al. Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions. IEEE Trans Syst Man Cybern Syst, 2016, 46: 1279–1286

    Article  Google Scholar 

  29. Duan X J, Zhi J H, Chen H M, et al. Two novel robust adaptive parameter estimation methods with prescribed performance and relaxed PE condition. Sci China Inf Sci, 2018, 61: 129203

    Article  MathSciNet  Google Scholar 

  30. Bechlioulis C P, Rovithakis G A. Robust partial-state feedback prescribed performance control of cascade systems with unknown nonlinearities. IEEE Trans Automat Contr, 2011, 56: 2224–2230

    Article  MathSciNet  MATH  Google Scholar 

  31. Kostarigka A K, Doulgeri Z, Rovithakis G A. Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity. Automatica, 2013, 49: 1137–1147

    Article  MathSciNet  MATH  Google Scholar 

  32. Bikas L N, Rovithakis G A. Combining prescribed tracking performance and controller simplicity for a class of uncertain MIMO nonlinear systems with input quantization. IEEE Trans Automat Contr, 2019, 64: 1228–1235

    Article  MathSciNet  MATH  Google Scholar 

  33. Wang D, Huang J. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw, 2005, 16: 195–202

    Article  Google Scholar 

  34. Du P H, Liang H J, Zhao S Y, et al. Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints. IEEE Trans Syst Man Cybern Syst, 2019. doi: https://doi.org/10.1109/TSMC.2019.2918351

    Google Scholar 

  35. Meng D Y, Moore K L. Robust cooperative learning control for directed networks with nonlinear dynamics. Automatica, 2017, 75: 172–181

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhang Y H, Liang H J, Ma H, et al. Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints. Appl Math Comput, 2018, 326: 16–32

    Article  MathSciNet  MATH  Google Scholar 

  37. Chen M, Tao G. Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone. IEEE Trans Cybern, 2016, 46: 1851–1862

    Article  Google Scholar 

  38. Su H Y, Chen M Z Q, Lam J, et al. Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Trans Circ Syst I, 2013, 60: 1881–1889

    MathSciNet  Google Scholar 

  39. 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: 666–672

    Article  Google Scholar 

  40. Zhang H W, Lewis F L. Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica, 2012, 48: 1432–1439

    Article  MathSciNet  MATH  Google Scholar 

  41. Wen G H, Yu W W, Xia Y Q, et al. Distributed tracking of nonlinear multiagent systems under directed switching topology: an observer-based protocol. IEEE Trans Syst Man Cybern Syst, 2017, 47: 869–881

    Article  Google Scholar 

  42. Li K W, Tong S C. Fuzzy adaptive practical finite-time control for time delays nonlinear systems. Int J Fuzzy Syst, 2019, 21: 1013–1025

    Article  MathSciNet  Google Scholar 

  43. Ge S S, Tee K P. Approximation-based control of nonlinear MIMO time-delay systems. Automatica, 2007, 43: 31–43

    Article  MathSciNet  MATH  Google Scholar 

  44. Bechlioulis C P, Rovithakis G A. Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Automat Contr, 2008, 53: 2090–2099

    Article  MathSciNet  MATH  Google Scholar 

  45. Kamali S, Tabatabaei S M, Arefi M M, et al. Prescribed performance adaptive neural output control for a class of switched nonstrict-feedback nonlinear time-delay systems: state-dependent switching law approach. Int J Robust Nonlin Control, 2019, 29: 1734–1757

    Article  MathSciNet  MATH  Google Scholar 

  46. Xie G, Sun L L, Wen T, et al. Adaptive transition probability matrix-based parallel IMM algorithm. IEEE Trans Syst Man Cybern Syst, 2019. doi: https://doi.org/10.1109/TSMC.2019.2922305

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by National Key R&D Program of China (Grant No. 2018YFB1700400), the Innovative Research Team Program of Guangdong Provincial Science Foundation (Grant No. 2018B030312006), and Science and Technology Program of Guangzhou (Grant No. 201904020006).

Author information

Authors and Affiliations

  1. School of Automation and Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, 510006, China

    Wenbin Xiao, Liang Cao, Hongyi Li & Renquan Lu

Authors
  1. Wenbin Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Renquan Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongyi Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, W., Cao, L., Li, H. et al. Observer-based adaptive consensus control for nonlinear multi-agent systems with time-delay. Sci. China Inf. Sci. 63, 132202 (2020). https://doi.org/10.1007/s11432-019-2678-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-019-2678-2

Keywords

Search

Navigation