[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Event-Triggered Optimal Nonlinear Systems Control Based on State Observer and Neural Network

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper develops a novel event-triggered optimal control approach based on state observer and neural network (NN) for nonlinear continuous-time systems. Firstly, the authors propose an online algorithm with critic and actor NNs to solve the optimal control problem and provide an event-triggered method to reduce communication and computation burdens. Moreover, the authors design weight estimation for critic and actor NNs based on gradient descent method and achieve uniformly ultimate boundednesss (UUB) estimation results. Furthermore, by using bounded NN weight estimation and dead-zone operator, the authors propose a triggering condition, prove the asymptotic stability of closed-loop system from Lyapunov stability perspective, and exclude the Zeno behavior. Finally, the authors provide a numerical example to illustrate the effectiveness of the proposed method.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Kim K H and Subbaraman C, Principles of constructing a timeliness-guaranteed kernel and time-triggered message-triggered object support mechanisms, Proceedings of 1st International Symposium on Object-Oriented Real-Time Distributed Computing, Kyoto, 1998.

  2. Tabuada P, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 2007, 52(9): 1680–1685.

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu X H, Tay W P, Liu Z W, et al., Quasi-synchronization of heterogeneous networks with a generalized Markovian topology and event-triggered communication, IEEE Transactions on Cybernetics, 2020, 50(10): 4200–4213.

    Article  Google Scholar 

  4. Heemels W P, Johansson K H, and Tabuada P, An introduction to event-triggered and self-triggered control, Proceedings of the 51st IEEE Conference on Decision and Control, Maui, 2012.

  5. Tiberi U and Johansson K H, A simple self-triggered sampler for perturbed nonlinear systems, Nonlinear Analysis: Hybrid Systems, 2013, 10(4): 126–140.

    MathSciNet  MATH  Google Scholar 

  6. Zhao Q T, Sun J, and Bai Y Q, Dynamic event-triggered control for nonlinear systems: A small-gain approach, Journal of Systems Science and Complexity, 2020, 33(4): 930–943.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang X and Chen M Y, Event-triggered consensus for second-order leaderless multi-agent systems, Proceedings of the 25th Chinese Control and Decision Conference, Guiyang, 2013.

  8. Fan Y, Liu L, Feng G, et al., Virtual neighbor based connectivity preserving of multi-agent systems with bounded control inputs in the presence of unreliable communication links, Automatica, 2013, 49(5): 1261–1267.

    Article  MathSciNet  MATH  Google Scholar 

  9. Fan Y, Yang Y, and Zhang Y, Sampling-based event-triggered consensus for multi-agent systems, Neurocomputing, 2016, 191(5): 141–147.

    Article  Google Scholar 

  10. Fan Y, Chen J, Song C, et al., Event-triggered coordination control for multi-agent systems with connectivity preservation, International Journal of Control, Automation and Systems, 2020, 18(4): 966–979.

    Article  Google Scholar 

  11. Fan Y, Zhang C X, and Song C, Sampling-based self-triggered coordination control for multi-agent systems with application to distributed generators, International Journal of Systems Science, 2018, 49(15): 3048–3062.

    Article  MathSciNet  MATH  Google Scholar 

  12. Fan Y, Feng G, Wang Y, et al., Distributed event-triggered control of multi-agent systems with combinational measurements, Automatica, 2013, 49(2): 671–675.

    Article  MathSciNet  MATH  Google Scholar 

  13. Xing M L and Deng F Q, Event-triggered sampled-data consensus of nonlinear multi-agent systems with control input losses, Journal of Systems Science & Complexity, 2018, 31(6): 1469–1497.

    Article  MathSciNet  MATH  Google Scholar 

  14. Sun J K, Yang J, Li S H, et al., Event-triggered output consensus disturbance rejection algorithm for multi-agent systems with time-varying disturbances, Journal of the Franklin Institute, 2020, 357(17): 12870–12885.

    Article  MathSciNet  MATH  Google Scholar 

  15. Shi P, Wang H J, and Lim C C, Network-based event-triggered control for singular systems with quantizations, IEEE Transactions on Industrial Electronics, 2016, 63(2): 1230–1238.

    Article  Google Scholar 

  16. Tian Y X, Yan H C, Zhang H, et al., Dynamic output-feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel, Automatica, 2020, 117(7): 108997–109004.

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang X F and Lemmon D X, On event design in event-triggered feedback systems, Automatica, 2011, 47(10): 2319–2322.

    Article  MathSciNet  MATH  Google Scholar 

  18. Ding D R, Wang D Z, Han Q L, et al., Neural-network-based output-feedback control under round-robin scheduling protocols, IEEE Transactions on Cybernetics, 2019, 49(6): 2372–2384.

    Article  Google Scholar 

  19. Almeida J, Silvestre C, and Pascoal A, Self-triggered state feedback control of linear plants under bounded disturbances, Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, 2010.

  20. Li B, Wang D Z, Ma F L, et al., Observer-based event-triggered control for nonlinear systems with mixed delays and disturbances: The input-to-state stability, IEEE Transactions on Cybernetics, 2019, 49(7): 2806–2819.

    Article  Google Scholar 

  21. Ma G Q, Liu X H, Pagilla P R, et al., Two-channel periodic event-triggered observer-based repetitive control for periodic reference tracking, Proceedings of the 44th Annual Conference of the IEEE Industrial Electronics Society, Washington, 2018.

  22. Chen X and Hao F, Observer-based event-triggered control for certain and uncertain linear systems, IMA Journal of Mathematical Control and Information, 2013, 30(4): 527–542.

    Article  MathSciNet  MATH  Google Scholar 

  23. Bian T, Jiang Y, and Jiang Z P, Adaptive dynamic programming for stochastic systems with state and control dependent noise, IEEE Transactions on Automatic Control, 2016, 61(12): 4170–4175.

    Article  MathSciNet  MATH  Google Scholar 

  24. Wei Q L, Liu D R, and Lin H Q, Value iteration adaptive dynamic programming for optimal control of discrete-time nonlinear systems, IEEE Transactions on Cybernetics, 2016, 46(3): 840–853.

    Article  Google Scholar 

  25. Dong L, Zhong X N, Sun C Y, et al., Event-triggered adaptive dynamic programming for continuous-time systems with control constraints, IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(8): 1941–1952.

    Article  MathSciNet  Google Scholar 

  26. Chen H H, Fan Y, and Chen J, Optimized event-triggered and self-triggered control for linear systems, Proceedings of the 34th Youth Academic Annual Conference of Chinese Association of Automation, Jinzhou, 2019.

  27. Vamvoudakis K G, Miranda M F, and Hespanha J P, Asymptotically stable adaptive optimal control algorithm with saturating actuators and relaxed persistence of excitation, IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(11): 2386–2398.

    Article  MathSciNet  Google Scholar 

  28. Vamvoudakis K G, Event-triggered optimal adaptive control algorithm for continuous-time nonlinear systems, IEEE/CAA Journal of Automatica Sinica, 2014, 1(3): 282–293.

    Article  Google Scholar 

  29. Yang X, He H B, and Liu D R, Event-triggered optimal neuro-controller design with reinforcement learning for unknown nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(9): 1866–1878.

    Article  Google Scholar 

  30. Yang X and Wei Q L, Adaptive critic learning for constrained optimal event-triggered control with discounted cost, IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(1): 91–104.

    Article  Google Scholar 

  31. Dong L, Yuan X, and Sun C Y, Event-triggered receding horizon control via actor-critic design, Science China Information Sciences, 2020, 63(5): 131–145.

    Article  MathSciNet  Google Scholar 

  32. Khalil H K, Nonlinear Systems, 3rd Ed., Prentice-Hall, Upper Saddle River, NJ, USA, 2002.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Anhui Engineering Laboratory of Human-Robot Integration System and Intelligent Equipment, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Songsong Cheng, Tianhong Pan & Yuan Fan

  2. Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Haoyun Li & Yuchao Guo

Authors
  1. Songsong Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haoyun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuchao Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tianhong Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuan Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan Fan.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61973002, 62103003, the Anhui Provincial Natural Science Foundation under Grant No. 2008085J32, the National Postdoctoral Program for Innovative Talents under Grant No. BX20180346, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2019M660834, and the Excellent Young Talents Program in Universities of Anhui Province under Grant No. gxyq2019002.

This paper was recommended for publication by Editor XIN Bin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, S., Li, H., Guo, Y. et al. Event-Triggered Optimal Nonlinear Systems Control Based on State Observer and Neural Network. J Syst Sci Complex 36, 222–238 (2023). https://doi.org/10.1007/s11424-022-1146-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-022-1146-0

Keywords

Search

Navigation