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Cooperative learning from adaptive neural control for a group of strict-feedback systems

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Abstract

This paper investigates the distributed cooperative learning (DCL) from adaptive neural network (NN) control for a group of strict-feedback systems, where the structure of all strict-feedback systems is identical. In order to achieve DCL easily, the system transformation method is employed for the strict-feedback systems. For an agent, only one radial basis function NN is used to approximate the lumped uncertainty in control design. Then the output tracking performance of all strict-feedback systems is guaranteed. What’s more, we prove that weights of all NNs in a multi-agent system converge to a small neighborhood around their common optimal value if the topology of the multi-agent system is connected and undirected. Thus, the approximation domain of all NNs is enlarged. Further, the previous learned NNs are used to improve the control performance. Finally, we provide two examples to demonstrate the effectiveness of the proposed scheme.

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References

  1. Krstic M, Kanellakopoulos I, Kokotovic P (1995) Nonlinear and adaptive control design. Wiley, New York

    MATH  Google Scholar 

  2. Shao X, Si H, Zhang W (2021) Event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors. Neural Comput Appl 33:5771–5791

    Article  Google Scholar 

  3. Yan H, Li Y (2017) Adaptive NN prescribed performance control for nonlinear systems with output dead zone. Neural Comput Appl 28:145–153

    Article  Google Scholar 

  4. Zhang T, Ge S, Hang C (2000) Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 6(12):1835–1846

    Article  MathSciNet  MATH  Google Scholar 

  5. Ge S, Wang C (2002) Direct adaptive NN control of a class of nonlinear systems. IEEE Trans Neural Netw 13(1):214–221

    Article  Google Scholar 

  6. Li J, Chen W, Li J (2011) Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems. Int J Robust Nonlinear Control 21:452–472

    Article  MathSciNet  MATH  Google Scholar 

  7. Tong S, Li Y (2012) Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans Fuzzy Syst 20(1):168–180

    Article  Google Scholar 

  8. Liu Y, Tong S (2017) Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76:143–152

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu J (2014) Observer-based backstepping dynamic surface control for stochastic nonlinear strict-feedback systems. Neural Comput Appl 24:1067–1077

    Article  Google Scholar 

  10. Wang W, Li Y (2019) Observer-based event-triggered adaptive fuzzy control for leader-following consensus of nonlinear strict-feedback systems. IEEE Trans Cybern 51(4):2131–2141

    Article  Google Scholar 

  11. Wang Z, Liu L, Wu Y, Zhang H (2018) Optimal fault-tolerant control for discrete-time nonlinear strict-feedback systems based on adaptive critic design. IEEE Trans Neural Netw Learn Syst 29(6):2179–2191

    Article  MathSciNet  Google Scholar 

  12. Zhang J, Yang G (2019) Low-complexity tracking control of strict-feedback systems with unknown control directions. IEEE Trans Autom Control 64(12):5175–5182

    Article  MathSciNet  MATH  Google Scholar 

  13. Song S, Zhang B, Song X, Zhang Z (2019) Neuro-fuzzy-based adaptive dynamic surface control for fractional-order nonlinear strict-feedback systems with input constraint. IEEE Trans Syst Man Cybern Syst 51(6):3575–3586

    Article  Google Scholar 

  14. Li H, Zhao S, He W, Lu R (2019) Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone. Automatica 100:99–107

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu B, Shou Y, Luo J, Pu H, Shi Z (2019) Neural learning control of strict-feedback systems using disturbance observer. IEEE Trans Neural Netw Learn Syst 30(5):1296–1307

    Article  MathSciNet  Google Scholar 

  16. Cui G, Jiao T, Wei Y, Song G, Chu Y (2014) Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation. Neural Comput Appl 25:779–791

    Article  Google Scholar 

  17. Liu L, Liu Y, Tong S (2019) Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems. IEEE Trans Cybern 49(7):2536–2545

    Article  Google Scholar 

  18. Wang D, Huang J (2005) Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw 16(1):195–202

    Article  Google Scholar 

  19. Li T, Wang D, Feng G, Tong S (2010) A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans Syst Man Cybern Part B Cybern 40(3):915–927

    Article  Google Scholar 

  20. Huang J (2015) Global adaptive neural dynamic surface control of strict-feedback systems. Neurocomputing 165:403–413

    Article  Google Scholar 

  21. Peng Z, Wang D, Wang J (2017) Predictor-based neural dynamic surface control for uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw Learn Syst 28(9):2156–2167

    Article  MathSciNet  Google Scholar 

  22. Xu B, Sun F (2018) Composite intelligent learning control of strict-feedback systems with disturbance. IEEE Trans Cybern 48(2):730–741

    Article  Google Scholar 

  23. Zhang T, Xia M, Yi Y (2017) Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics. Automatica 81:232–239

    Article  MathSciNet  MATH  Google Scholar 

  24. Chen M, Tao G, Jiang B (2015) Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans Neural Netw Learn Syst 26(9):2086–2097

    Article  MathSciNet  Google Scholar 

  25. Wang M, Wang C (2015) Learning from adaptive neural dynamic surface control of strict-feedback systems. IEEE Trans Neural Netw Learn Syst 26(6):1247–1259

    Article  MathSciNet  Google Scholar 

  26. Swaroop D, Hedrick J, Yip P, Gerdes J (2000) Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Control 45(10):1893–1899

    Article  MathSciNet  MATH  Google Scholar 

  27. Yip P, Hedrick J (1998) Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int J Control 71(5):959–979

    Article  MathSciNet  MATH  Google Scholar 

  28. Song B, Hedrick J (2004) Observer-based dynamic surface control for a class of nonlinear systems: an LMI approach. IEEE Trans Autom Control 49(11):1995–2001

    Article  MathSciNet  MATH  Google Scholar 

  29. Park J, Kim S, Moon C (2009) Adaptive neural control for strict-feedback nonlinear systems without backstepping. IEEE Trans Neural Netw 20(7):1204–1209

    Article  Google Scholar 

  30. Wang C, Hill D (2006) Learning from neural control. IEEE Trans Neural Netw 17(1):130–146

    Article  Google Scholar 

  31. Liu T, Wang C, Hill DJ (2009) Learning from neural control of nonlinear systems in normal form. Syst Control Lett 58(9):633–638

    Article  MathSciNet  MATH  Google Scholar 

  32. Dai S, Wang C, Wang M (2014) Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems. IEEE Trans Neural Netw Learn Syst 25(1):111–123

    Article  Google Scholar 

  33. Wang M, Wang C (2015) Neural learning control of pure-feedback nonlinear systems. Nonlinear Dyn 79:2589–2608

    Article  MathSciNet  Google Scholar 

  34. Wang M, Wang C, Shi P, Liu X (2016) Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance. IEEE Trans Neural Netw Learn Syst 27(12):2564–2576

    Article  MathSciNet  Google Scholar 

  35. Wang M, Yang A (2017) Dynamic learning from adaptive neural control of robot manipulators with prescribed performance. IEEE Trans Syst Man Cybern Syst 47(8):2244–2255

    Article  Google Scholar 

  36. Dai S, He S, Wang M, Yuan C (2019) Adaptive neural control of underactuated surface vessels with prescribed performance guarantees. IEEE Trans Neural Netw Learn Syst 30(12):3686–3698

    Article  MathSciNet  Google Scholar 

  37. Chen W, Hua S, Zhang H (2015) Consensus-based distributed cooperative learning from closed-loop neural control systems. IEEE Trans Neural Netw Learn Syst 26(2):331–345

    Article  MathSciNet  Google Scholar 

  38. Ai W, Chen W, Hua S (2018) Distributed cooperative learning for a group of uncertain systems via output feedback and neural networks. J Frankl Inst 355(5):2536–2561

    Article  MathSciNet  MATH  Google Scholar 

  39. Yuan C, He H, Wang C (2019) Cooperative deterministic learning-based formation control for a group of nonlinear uncertain mechanical systems. IEEE Trans Ind Inform 15(1):319–333

    Article  Google Scholar 

  40. Gao F, Chen W, Li Z, Li J, Xu B (2020) Neural network-based distributed cooperative learning control for multiagent systems via event-triggered communication. IEEE Trans Neural Netw Learn Syst 31(2):407–419

    Article  MathSciNet  Google Scholar 

  41. Laub A (2005) Matrix analysis for scientists and engineers. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  42. Park J, Sandberg I (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

    Article  Google Scholar 

  43. Sanner R, Slotine J (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3(6):837–863

    Article  Google Scholar 

  44. Cui B, Xia Y, Liu K, Shen G (2020) Finite-time tracking control for a class of uncertain strict-feedback nonlinear systems with state constraints: a smooth control approach. IEEE Trans Neural Netw Learn Syst 31(11):4920–4932

    Article  MathSciNet  Google Scholar 

  45. Bthtash S (1990) Robust output tracking for non-linear systems. Int J Control 51(6):1381–1407

    Article  Google Scholar 

  46. Ge SS, Hang CC, Lee T, Zhang T (2001) Stable adaptive neural network control. Kluwer, Norwell

    MATH  Google Scholar 

  47. Yang YS, Ren JS (2003) Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans Fuzzy Syst 11(6):783–795

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61966026, 61941304 and 61673014, 62163030, and in part by Natural Science Foundation of Inner Mongolia under Grants 2020BS06004 and 2019BS06006.

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Authors and Affiliations

  1. College of Electronic Information Engineering, Inner Mongolia University, Hohhot, 010021, China

    Fei Gao, Fengshan Bai, Zhi Weng & Xitai Na

  2. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Jing Li

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  1. Fei Gao
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  2. Fengshan Bai
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Correspondence to Fei Gao.

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Gao, F., Bai, F., Weng, Z. et al. Cooperative learning from adaptive neural control for a group of strict-feedback systems. Neural Comput & Applic 34, 14435–14449 (2022). https://doi.org/10.1007/s00521-022-07239-9

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  • DOI: https://doi.org/10.1007/s00521-022-07239-9

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