Advertisement

Finite Time Controller Design of Nonlinear Quantized Systems with Nonstrict Feedback Form

  • Xueyi Zhang
  • Fang WangEmail author
  • Lili Zhang
Regular Papers Intelligent Control and Applications
  • 20 Downloads

Abstract

This article considers a finite-time control problem of nonlinear quantized systems in complex environments. The controlled system is in a non-strict feedback form. By applying a nonlinear decomposition of hysteretic quantizer, the quantization issue is tackled successfully. By employing a structural property of radial basis function (RBF) neural networks (NNs), the conventional backstepping method is extended to non-strict feedback nonlinear quantized systems. Based on the finite time stability criterion, a new adaptive neural control scheme is presented. The constructed neural controller can ensure the transient performance of nonlinear quantized systems.

Keywords

Adaptive control finite-time control neural network quantized nonlinear systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. Yang, Y. Jiang, Z. Li, W. He, and C. Su, “Neural control of bimanual robots with guaranteed global stability and motion precision,” IEEE Transactions on Industrial Informatics, vol. 13, no. 3, pp. 1162–1171, 2017.Google Scholar
  2. [2]
    W. He, Z. J. Li, and C. L. Philip Chen, “A survey of human–centered intelligent robots: Issues and challenges,” IEEE/CAA Jouirnal of Automatica Sinica, vol. 4, no. 4, pp. 602–609, Oct. 2017.Google Scholar
  3. [3]
    W. He, Z. C. Yan, and C. Y. Sun, “Adaptive neural network control of a flapping wing micro aerial vehicle with distur bance observer,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3452–3465, 2017.Google Scholar
  4. [4]
    C. Yang, X. Wang, Z. Li, Y. Li, and C. Y. Su, “Teleoperation control based on combination of wave variable and neural networks,” IEEE Trans. Syst., Man, Cybern., Syst., vol. 47, no. 8, pp. 2125–2136, 2017.Google Scholar
  5. [5]
    W. He, Z. C. Yan, Y. K. Sun, Y. S. Qu, and C. Y. Sun, “Neural–learning–based control for a constrained robotic manipulator with flexible joints,” IEEE Trans Neural Netw Learn Syst., vol. 29, no. 12, pp. 5993–6003, 2018.Google Scholar
  6. [6]
    Y. L. Wei, J. H. Park, H. R. Karimi, Y. C. Tian, and H. Jung, “Improved stability and stabilization results for stochastic synchronization of continuous–time semi–Markovian jump neural networks with time–varying delay,” IEEE Trans Neural Netw Learn Syst., vol. 29, no. 6, pp. 2488–2501, 2018.MathSciNetGoogle Scholar
  7. [7]
    C. Y. Sun, W. He, and W. L. Ge, “Adaptive neural network control of biped robots,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 2, pp. 315–326, 2017.Google Scholar
  8. [8]
    H. Gao, W. He, C. Zhou, and C. Sun, “Neural network control of a two–link flexible robotic manipulator using assumed mode method,” IEEE Trans. Ind. Inform., pp. 1–1, March 2018. DOI: 10.1109/TII.2018.2818120Google Scholar
  9. [9]
    N. Elia and S. Mitter, “Stabilization of linear systems with limited information,” IEEE Trans. Autom. Control, vol. 46, no. 9, pp. 1384–1400, Sep. 2001.MathSciNetzbMATHGoogle Scholar
  10. [10]
    S. Tatikonda and S. Mitter, “Control under communication constraints,” IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1056–1068, Jul. 2004.MathSciNetzbMATHGoogle Scholar
  11. [11]
    H. Ma, Q. Zhou, L. Bai, and H. Liang, “Observerbased adaptive fuzzy fault–tolerant control for stochastic nonstrict–feedback nonlinear systems with input quantization,” IEEE Transactions on Systems, Man and Cybernetics: Systems, pp. 1–12, June 2018. DOI: 10.1109/TSMC.2018.2833872Google Scholar
  12. [12]
    C. Persis and A. Isidori, “Stabilizability by state feedback implies stabilizability by encoded state feedback,” Syst. Control Lett., vol. 53, pp. 249–258, 2004.MathSciNetzbMATHGoogle Scholar
  13. [13]
    D. Liberzon and J. Hespanha, “Stabilization of nonlinear systems with limited information feedback,” IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 910–915, Jun. 2005.MathSciNetzbMATHGoogle Scholar
  14. [14]
    H. Gao and T. Chen, “A new approach to quantized feedback control systems,” Automatica, vol. 44, no. 2, pp. 534–542, 2008.MathSciNetzbMATHGoogle Scholar
  15. [15]
    H. Gao, X. Meng, and T. Chen, “Stabilization of networked control systems with a new delay characterization,” IEEE Trans. Autom. Control, vol. 53, no. 9, pp. 2142–2148, 2008.MathSciNetzbMATHGoogle Scholar
  16. [16]
    T. Hayakawaa, H. Ishii, and K. Tsumurac, “Adaptive quantized control for linear uncertain discrete–time systems,” Automatica, vol. 45, pp. 692–700, 2009.MathSciNetGoogle Scholar
  17. [17]
    H. Sun, N. Hovakimyan, and T. Basar, “L1 adaptive controller for systems with input quantization,” Proc. of Amer. Control Conf., Baltimore, MD, USA, pp. 253–258. Jun, 2010.Google Scholar
  18. [18]
    T. Hayakawaa, H. Ishii, and K. Tsumurac, “Adaptive quantized control for nonlinear uncertain systems,” Syst. Control Lett., vol. 58, pp. 625–632, 2009.MathSciNetGoogle Scholar
  19. [19]
    J. Zhou, C. Wen, and G. Yang, “Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal,” IEEE Trans. Autom. Control, vol. 59, no. 2, pp. 460–464, Feb. 2014.MathSciNetzbMATHGoogle Scholar
  20. [20]
    Z. Liu, F. Wang, Y. Zhang, and C. L. Philip Chen, “Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems,” IEEE Trans. Cybern., vol. 46, no. 2, pp. 524–534, 2016.Google Scholar
  21. [21]
    F. Wang, Z. Liu, Y. Zhang, and C. L. Philip Chen, “Adaptive quantized controller design via backstepping and stochastic small–gain approach,” IEEE Trans. Fuzzy Syst., vol. 24, no. 2, pp. 330–343, 2016.Google Scholar
  22. [22]
    Y. Tang, “Terminal sliding mode control for rigid robots,” Automatica, vol. 34, no. 1, pp. 51–56, 1998.MathSciNetzbMATHGoogle Scholar
  23. [23]
    C. Tan, X. Yu, and Z. Man, “Terminal sliding mode observers for a class of nonlinear systems,” Automatica, vol. 46, no. 8, pp. 1401–1404, 2010.MathSciNetzbMATHGoogle Scholar
  24. [24]
    S. P. Bhat and D. S. Bernstein, “Continuous finite–time stabilization of the translational and rotational double integrators,” IEEE Trans. Autom. Control, vol. 43, no. 5, pp. 678–682, 1998.MathSciNetzbMATHGoogle Scholar
  25. [25]
    S. P. Bhat and D. S. Bernstein, “Finite–time stability of continuous autonomous systems,” SIAM J. Control Optim., vol. 38, no. 3, pp. 751–766, 2000.MathSciNetzbMATHGoogle Scholar
  26. [26]
    X. Huang, W. Lin, and B. Yang, “Global finite–time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, 2005.MathSciNetzbMATHGoogle Scholar
  27. [27]
    Y. Hong, J. Wang, and D. Cheng, “Adaptive finite–time control of nonlinear systems with parametric uncertainty,” IEEE Trans. Autom. Control, vol. 51, no. 5, pp. 858–862, 2006.MathSciNetzbMATHGoogle Scholar
  28. [28]
    C. Yang, Y. Jiang, W. He, J. Na, Z. Li, and B. Xu, “Adaptive parameter estimation and control design for robot manipulators with finite–time convergence,” IEEE Trans. Ind. Electron., vol. 65, no. 10, pp. 8112–8123, Oct. 2018.Google Scholar
  29. [29]
    F. Wang, B. Chen, Y. M. Sun, and C. Lin, “Finite time control of switched stochastic nonlinear systems,” Fuzzy Sets Syst., 2018. DOI: 10.1016/j.fss.2018.04.016Google Scholar
  30. [30]
    Y. J. Cui, W. J. Ma, Q. Sun, and X. Su, “New uniqueness results for boundary value problem of fractional differential equation,” Nonlinear Analysis: Modelling and Control, vol. 23, no. 1, pp. 31–39, 2018.MathSciNetGoogle Scholar
  31. [31]
    S. Ding, S. Li, and W. X. Zheng, “Nonsmooth stabilization of a class of nonlinear cascaded systems,” Automatica, vol. 48, no. 10, pp. 2597–2606, 2012.MathSciNetzbMATHGoogle Scholar
  32. [32]
    W. Lv and F. Wang, “Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks,” Adv. Differ. Equ., vol. 2017. pp. 374–390, 2017.MathSciNetGoogle Scholar
  33. [33]
    J. M. Wang, H. D. Cheng, Y. Li, and X. N. Zhang, “The geometrical analysis of a predator–prey model with multistate dependent impulses,” J. Appl. Anal. Comput., vol. 8, no. 2, pp. 427–442, 2018.MathSciNetGoogle Scholar
  34. [34]
    J. Wang, H. Cheng, H. Liu, and Y. Wang, “Periodic solution and control optimization of a prey–predator model with two types of harvesting,” Adv. Differ. Equ., vol. 2018. pp. 41–54, 2018.MathSciNetGoogle Scholar
  35. [35]
    Y. Li, H. Cheng, J. Wang, and Y. Wang, “Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy,” Adv. Differ. Equ., vol. 2018. pp. 32–45, 2018.MathSciNetGoogle Scholar
  36. [36]
    F. Liu and H. Wu, “Regularity of discrete multisublinear fractional maximal functions,” Sci. China Math., vol. 60, no. 8, pp. 1461–1476, 2017.MathSciNetzbMATHGoogle Scholar
  37. [37]
    F. Liu, “Continuity and approximate differentiability of multisublinear fractional maximal functions,” Math. Inequal. Appl., vol. 21, no. 1, pp. 25–40, 2018.MathSciNetzbMATHGoogle Scholar
  38. [38]
    W. Lv, F. Wang, and Y. Li, “Adaptive finite–time tracking control for nonlinear systems with unmodeled dynamics using neural networks,” Adv. Differ. Equ., vol. 2018. pp. 159–175, 2018.MathSciNetGoogle Scholar
  39. [39]
    Q. Y. Su and X. L. Jia, “Finite–time H¥ control of cascade nonlinear switched systems under state–dependent switching,” Int. J. Control Autom. Syst., vol. 16, no. 1, pp. 120–128, 2018.Google Scholar
  40. [40]
    Q. H. Meng, Z. Y. Sun, and Y. S. Li, “Finite–time controller design for four–wheel–steering of electric vehicle driven by four in–wheel motors,” Int. J. Control Autom. Syst., vol. 16, no. 4, pp. 1814–1823, 2018.Google Scholar
  41. [41]
    R. C. Ma, B. Jiang, and Y. Liu, “Finite–time stabilization with output–constraints of a class of highorder nonlinear systems,” Int. J. Control Autom. Syst., vol. 16, no. 3, pp. 945–952, 2018.Google Scholar
  42. [42]
    G. D. Zong, X. H. Wang, and H. J. Zhao, “Robust finitetime guaranteed cost control for impulsive switched systems with time–varying delay,” Int. J. Control Autom. Syst., vol. 15, no. 1, pp. 113–121, 2017.Google Scholar
  43. [43]
    H. H. Dong, T. T. Chen, L. F. Chen, and Y. Zhang, “A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations,” J. Nonlinear Sci. Appl., vol. 9, pp. 5107.5118, 2016.Google Scholar
  44. [44]
    F.Wang, X. Y. Zhang, B. Chen, C. Lin, X. Li, and J. Zhang, “Adaptive finite–time tracking control of switched nonlinear systems,” Information Sciences, vol. 421, pp. 126–135, 2017.MathSciNetGoogle Scholar
  45. [45]
    F. F. Bian, W. C. Zhao, Y. Song, and R. Yue, “Dynamical analysis of a class of prey–predator model with Beddington–DeAngelis functional response, stochastic perturbation, and impulsive toxicant input,” Complexity, vol. 2017, no. 3, pp. 1–18, 2017.zbMATHGoogle Scholar
  46. [46]
    C. D. Li, J. L. Gao, J. Q. Yi, and G. Q. Zhang, “Analysis and design of functionally weighted single–input–rulemodules connected fuzzy inference systems,” IEEE Trans. Fuzzy Syst., vol. 26, no. 1, pp. 56–71, 2018.Google Scholar
  47. [47]
    C. D. Li, Z. X. Ding, D. B. Zhao, J. Yi, and G. Zhang, “Building energy consumption prediction: an extreme deep learning approach,” Energies, vol. 10, no. 10, pp. 1–20, Oct. 2017.Google Scholar
  48. [48]
    Y. J. Liang, R. Ma, M. Wang, and J. Fu, “Global finite–time stabilisation of a class of switched nonlinear systems,” Int. J. Syst. Sci. vol. 46, no. 16, pp. 2897.2904, 2015.Google Scholar
  49. [49]
    F. Wang, B. Chen, C. Lin, J. Zhang, and X. Z. Meng, “Adaptive neural network finite–time output feedback control of quantized nonlinear systems,” IEEE Trans. Cybern., vol. 48, no. 6, pp. 1839–1848, 2018.Google Scholar
  50. [50]
    B. Niu, D. Wang, H. Li, X. Xie, N. D. Alotaibi, and F. E. Alsaadi, “A novel neural–network–based adaptive control scheme for output–constrained stochastic switched nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–15, 2017. DOI: 10.1109/TSMC.2017.2777472Google Scholar
  51. [51]
    B. Niu, D.Wang, N. D. Alotaibi, and F. E. Alsaadi, “Adaptive neural state–feedback tracking control of stochastic nonlinear switched systems: an average dwell–time method,” IEEE Trans. Neural Netw., pp. 1–12, 2018. DOI:10.1109/TNNLS.2018.2860944Google Scholar
  52. [52]
    J. Huang, C. Wen, W. Wang, and Y.–D. Song, “Design of adaptive finite–time controllers for nonlinear uncertain systems based on given transient specifications,” Automatica, vol. 69, no. 1, pp. 395–404, 2016.MathSciNetzbMATHGoogle Scholar
  53. [53]
    X. P. Li, X. Y. Lin, and Y. Q. Lin, “Lyapunov–type conditions and stochastic differential equations driven by GBrownian motion,” J. Math. Anal. Appl., vol. 439, no. 1, pp. 235–255, 2016.MathSciNetzbMATHGoogle Scholar
  54. [54]
    Y. Yang, C. Hua, and X. Guan, “Adaptive fuzzy finite–time coordination control for networked nonlinear bilateral teleoperation system,” IEEE Trans. Fuzzy Syst., vol. 22, no. 3, pp. 631–641, 2014.Google Scholar
  55. [55]
    J. Wu, W. S. Chen, and J. Li, “Global finite–time adaptive stabilization for nonlinear systems with multiple unknown control directions,” Automatica, vol. 69, no. 1, pp. 298–307, 2016.MathSciNetzbMATHGoogle Scholar
  56. [56]
    F.Wang, B. Chen, X. P. Liu, and C. Lin, “Finite–time adaptive fuzzy tracking control design for nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 26, no. 3, pp. 1207–1216, 2018.Google Scholar
  57. [57]
    Z. Zhu, Y. Q. Xia, and M. Y. Fu, “Attitude stabilization of rigid spacecraft with finite–time convergence,” Int. J. Robust Nonlinear Control, vol. 21, pp. 686–702, 2011.MathSciNetzbMATHGoogle Scholar
  58. [58]
    W. Liu, D. W. C Ho, and S. Xu, “Adaptive finite–time stabilization of a class of quantized nonlinearly parameterized systems,” Int. J. Robust Nonlinear Control, vol. 27, no. 18, pp. 4554–4573, 2017.MathSciNetzbMATHGoogle Scholar
  59. [59]
    C. Wen, J. Zhou, Z. Liu, and H. Su, “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Trans. Autom. control, vol. 56, no. 7, pp. 1672–1678, 2011.MathSciNetzbMATHGoogle Scholar
  60. [60]
    J. P. Cai, C. Y. Wen, H. Y. Su, Z. Liu, and L. Xing, “Adaptive backstepping control for a class of nonlinear systems with non–triangular structural uncertainties,” IEEE Trans. Autom. control, vol. 62, no. 10, pp. 5220–5226, 2017.MathSciNetzbMATHGoogle Scholar
  61. [61]
    G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.zbMATHGoogle Scholar
  62. [62]
    C. Qian and W. Lin, “Non–Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization,” Syst. Control Lett., vol. 42, no. 3, pp. 185–200, 2001.MathSciNetzbMATHGoogle Scholar
  63. [63]
    H. Q. Wang, P. Shi, H. Li, and Q. Zhou, “Adaptive neural tracking control for a class of nonlinear systems with unmodeled dynamics,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3075–3087, 2017.Google Scholar
  64. [64]
    F. Wang, B. Chen, C. Lin, and X. H. Li, “Distributed adaptive neural control for stochastic nonlinear multiagent systems,” IEEE Trans. Cybern., vol. 47.no. 7, pp. 1795.1803, 2017.Google Scholar
  65. [65]
    Y. Wei, J. H. Park, J. Qiu, L. Wu, and H. Y. Jung, “Sliding mode control for semi–Markovian jump systems via output feedback,” Automatica, vol. 81, pp. 133–141, 2017.MathSciNetzbMATHGoogle Scholar
  66. [66]
    Y. L. Wei, J. B. Qiu, P. Shi, and M. ChaDli, “Fixed–order piecewise–affine output feedback controller for fuzzyaffine–model–based nonlinear systems with time–varying delay,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 64, no. 4, pp. 945–958, 2017.Google Scholar
  67. [67]
    Y. J. Liu, M. Z. Gong, S. C. Tong, C. L. P. Chen, and D. J. Li, “Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints,” IEEE Trans. Fuzzy Syst., vol. 26, no. 5, pp. 2607–2617, Oct. 2018.Google Scholar
  68. [68]
    L. Liu, Z. Wang, and H. Zhang, “Adaptive fault–tolerant tracking control for MIMO discrete–time systems via reinforcement learning algorithm with less learning parameters,” IEEE Trans. Autom. Sci. Eng., vol. 14, no. 1, pp. 299–313, 2017.Google Scholar
  69. [69]
    F. Wang and X. Y. Zhang, “Adaptive finite time control of nonlinear systems under time–varying actuator failures,” IEEE Trans. Syst., Man, Cybern., Syst., DOI:10.1109/TSMC.2018.2868329.Google Scholar
  70. [70]
    J. B. Qiu, Y. L. Wei, H. R. Karimi, and H. Gao, “Reliable control of discrete–time piecewise–affine time–delay systems via output feedback,” IEEE Trans. Rel., vol. 67, no. 1, pp. 79–91, 2018.Google Scholar
  71. [71]
    C. Wang, C. Wen, and L. Guo, “Decentralized outputfeedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures,” Automatica, vol. 71, pp. 187–196, 2016.MathSciNetzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Foreign LanguagesShandong University of Science and TechnologyQingdaoChina
  2. 2.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoP. R. China
  3. 3.School of Applied MathematicsGuangdong University of TechnologyGuangzhouP. R. China

Personalised recommendations