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Robust Adaptive Sampled-Data Control Scheme for a Class of Uncertain Nonlinear Systems

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Abstract

In this paper, a simple robust adaptive sampled-data control law is addressed for a class of uncertain continuous-time systems. For achieving this goal, firstly, the regulation problem and \( H_{\infty } \) control designs would be formulated in the uncertain continuous-time systems via including a sampler and data-hold circuits. Then, a robust adaptive digital control law will be derived by using the discrete-time Lyapunov’s stability theory. The results are numerically implemented in two nonlinear uncertain systems. The simulations show the effectiveness of the proposed robust adaptive digital control method compared with the other techniques.

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References

  1. K.J. Åström, B. Wittenmark, Adaptive control, 2nd edn. (Courier Corporation, North Chelmsford, 1995)

    MATH  Google Scholar 

  2. W. Bai, Q. Zhou, T. Li, H. Li, Adaptive reinforcement learning neural network control for uncertain nonlinear system with input saturation. IEEE Trans. Cybern. 50(8), 3433–3443 (2019)

    Article  Google Scholar 

  3. W. Bai, T. Li, S. Tong, NN reinforcement learning adaptive control for a class of nonstrict-feedback discrete-time systems. IEEE Trans. Cybern. 50(11), 4573–4584 (2020)

    Article  Google Scholar 

  4. Y. Cao, L. Zhang, C. Li, M.Z.Q. Chen, Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology. IEEE Trans. Cybern. 47(8), 2212–2222 (2017)

    Article  Google Scholar 

  5. D.-Y. Chen, C. Wu, C.-F. Liu, X.-Y. Ma, Y.-J. You, R.-F. Zhang, Synchronization and circuit simulation of a new double-wing chaos. Nonlinear Dyn. 67(2), 1481–1504 (2012)

    Article  Google Scholar 

  6. D. Chen, C. Ding, Y. Do, X. Ma, H. Zhao, Y. Wang, Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control. J. Franklin Inst. 351(9), 4596–4618 (2014)

    Article  Google Scholar 

  7. M. Chen, S.S. Ge, B.V.E. How, Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans. Neural Netw. 21(5), 796–812 (2010)

    Article  Google Scholar 

  8. M. Chen, X. Wang, Flocking dynamics for multi-agent system with measurement delay. Math. Comput. Simul. 171, 187–200 (2020)

    Article  MathSciNet  Google Scholar 

  9. H. Du, C. Qian, S. Li, Z. Chu, Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems. Automatica 99, 403–411 (2019)

    Article  MathSciNet  Google Scholar 

  10. M. Elmi, H.A. Talebi, M.B. Menhaj, Robust adaptive dynamic surface control of nonlinear time-varying systems in strict-feedback form. Int. J. Control Autom. Syst. 17(6), 1432–1444 (2019)

    Article  Google Scholar 

  11. J. Fu, R. Ma, T. Chai, Adaptive finite-time stabilization of a class of uncertain nonlinear systems via logic-based switchings. IEEE Trans. Autom. Control 62(11), 5998–6003 (2017)

    Article  MathSciNet  Google Scholar 

  12. V. Ghaffari, P. Karimaghaee, Design of adaptive discrete time controller for a class of nonlinear systems. Nonlinear Stud. 19(1), 149–159 (2012)

    MathSciNet  MATH  Google Scholar 

  13. V. Ghaffari, A. Razminia, M. Mirzaei, Improved robust adaptive control law for a class of uncertain nonlinear systems and its application to chaotic systems. Iran. J. Sci. Technol. Trans. Electr. Eng. 43, 741–756 (2019)

    Article  Google Scholar 

  14. R. Goebel, R.G. Sanfelice, A.R. Teel, Hybrid dynamical systems. IEEE Control Syst. Mag. 29(2), 28–93 (2009)

    Article  MathSciNet  Google Scholar 

  15. Y. Guan, Y. Wu, H. Wu, Y. Li, S. He, Synchronization of complex dynamical networks with actuator saturation by using sampled-data control. Circuits Syst. Signal Process. 38(12), 5508–5527 (2019)

    Article  Google Scholar 

  16. C. Hua, X. Guan, Adaptive control for chaotic systems. Chaos Solitons Fractals 22(1), 55–60 (2004)

    Article  MathSciNet  Google Scholar 

  17. C. Hua, S. Wu, X. Guan, Stabilization of TS fuzzy system with time delay under sampled-data control using a new looped-functional. IEEE Trans. Fuzzy Syst. 28(2), 400–407 (2019)

    Article  Google Scholar 

  18. A. Ilchmann, E.P. Ryan, On gain adaptation in adaptive control. IEEE Trans. Autom. Control 48(5), 895–899 (2003)

    Article  MathSciNet  Google Scholar 

  19. F. Jia, X. Yan, X. Wang, J. Lu, Y. Li, Robust adaptive prescribed performance dynamic surface control for uncertain nonlinear pure-feedback systems. J. Franklin Inst. 357(5), 2752–2772 (2020)

    Article  MathSciNet  Google Scholar 

  20. H.K. Khalil, Nonlinear systems, 3rd edn. (Prentice Hall, Upper Saddle River, 2002)

    MATH  Google Scholar 

  21. D.S. Laila, D. Nešić, A. Astolfi, Sampled-data control of nonlinear systems, in Advanced Topics in Control Systems Theory (Springer, 2006), pp. 91–137

  22. Y.-X. Li, G.-H. Yang, Robust adaptive fault-tolerant control for a class of uncertain nonlinear time delay systems. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1554–1563 (2016)

    Article  Google Scholar 

  23. Y.-X. Li, G.-H. Yang, Observer-based fuzzy adaptive event-triggered control codesign for a class of uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1589–1599 (2017)

    Article  MathSciNet  Google Scholar 

  24. D. Nešić, A.R. Teel, Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model. Automatica 42(10), 1801–1808 (2006)

    Article  MathSciNet  Google Scholar 

  25. R. Rakkiyappan, N. Sakthivel, Stochastic sampled-data control for exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay. Circuits Syst. Signal Process. 34(1), 153–183 (2015)

    Article  MathSciNet  Google Scholar 

  26. R. Rakkiyappan, V.P. Latha, K. Sivaranjani, Exponential H synchronization of Lur’e complex dynamical networks using pinning sampled-data control. Circuits Syst. Signal Process. 36(10), 3958–3982 (2017)

    Article  Google Scholar 

  27. Q. Shen, P. Shi, S. Wang, Y. Shi, Fuzzy adaptive control of a class of nonlinear systems with unmodeled dynamics. Int. J. Adapt. Control Signal Process. 33(4), 712–730 (2019)

    Article  MathSciNet  Google Scholar 

  28. E.D. Sontag, Input to state stability: basic concepts and results, in Nonlinear and Optimal Control Theory (Springer, 2008), pp. 163–220

  29. W. Sun, Y. Zhang, Y. Huang, H. Gao, O. Kaynak, Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems. IEEE Trans. Industr. Electron. 63(10), 6510–6518 (2016)

    Article  Google Scholar 

  30. R. Wang, J. Xing, C. Zhou, P. Wang, Q. Yang, Finite-time asynchronously switched control of switched systems with sampled-data feedback. Circuits Syst. Signal Process. 33(12), 3713–3738 (2014)

    Article  Google Scholar 

  31. C. Wen, J. Zhou, Z. Liu, H. Su, Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans. Autom. Control 56(7), 1672–1678 (2011)

    Article  MathSciNet  Google Scholar 

  32. L. Xing, C. Wen, H. Su, Z. Liu, J. Cai, Robust control for a class of uncertain nonlinear systems with input quantization. Int. J. Robust Nonlinear Control 26(8), 1585–1596 (2016)

    Article  MathSciNet  Google Scholar 

  33. L. Xing, C. Wen, Y. Zhu, H. Su, Z. Liu, Output feedback control for uncertain nonlinear systems with input quantization. Automatica 65, 191–202 (2016)

    Article  MathSciNet  Google Scholar 

  34. L. Xing, C. Wen, Z. Liu, H. Su, J. Cai, Event-triggered output feedback control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 64(1), 290–297 (2018)

    Article  MathSciNet  Google Scholar 

  35. J. Yang, J. Na, G. Gao, Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence. Int. J. Adapt. Control Signal Process. 33(12), 1868–1884 (2019)

    Article  MathSciNet  Google Scholar 

  36. W. Zhang, Q.-L. Han, Y. Tang, Y. Liu, Sampled-data control for a class of linear time-varying systems. Automatica 103, 126–134 (2019)

    Article  MathSciNet  Google Scholar 

  37. J. Zhou, C. Wen, W. Wang, Adaptive control of uncertain nonlinear systems with quantized input signal. Automatica 95, 152–162 (2018)

    Article  MathSciNet  Google Scholar 

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Correspondence to Valiollah Ghaffari.

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Ghaffari, V. Robust Adaptive Sampled-Data Control Scheme for a Class of Uncertain Nonlinear Systems. Circuits Syst Signal Process 40, 2282–2301 (2021). https://doi.org/10.1007/s00034-020-01586-5

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