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Adaptive Fuzzy Output Feedback Control for Nonlinear Nonstrict-Feedback Time-Delay Systems with Full State Constraints

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Abstract

This paper investigates the adaptive fuzzy output feedback control problem for a class of nonstrict-feedback time-delay systems subject to full state constraints. An observer is designed to estimate the unavailable systems states. By incorporating the barrier Lyapunov function and introducing a variable separation approach, an adaptive fuzzy output feedback tracking controller is systematically designed to ensure that the full state constraints are not violated and all the signals of the closed-loop systems are uniformly ultimately bounded. At the same time, the tracking errors can fluctuate around the origin within a small neighborhood by appropriate choice of the design parameters. Finally, two simulation studies are worked out to show the effectiveness of the proposed approach.

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References

  1. Gilbert, E., Kolmanovsky, I.: Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor. Automatica 38(12), 2063–2073 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hu, T., Lin, Z.: Control systems with actuator saturation: analysis and design. Birkhauser, Boston (2001)

    Book  MATH  Google Scholar 

  3. Zhou, B., Duan, G.R., Lin, Z.: A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. Automatica 47(2), 316–325 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhou, B., Li, Z.Y., Lin, Z.: Discrete-time l ∞and l 2 norm vanishment and low gain feedback with their applications in constrained control. Automatica 49(1), 111–123 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, M., Ge, S.S., Ren, B.: Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica 47(3), 452–465 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ren, B., Ge, S.S., Tee, K.P., Lee, T.H.: Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans. Neural Netw. 21(8), 1339–1345 (2010)

    Article  Google Scholar 

  7. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tee, K.P., Ren, B., Ge, S.S.: Control of nonlinear systems with time-varying output constraints. Automatica 47(11), 2511–2516 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tee, K.P., Ge, S.S., Tay, F.E.H.: Adaptive control of electrostatic microactuators with bidirectional drive. IEEE Trans. Control. Syst. Technol. 17(2), 340–352 (2009)

    Article  Google Scholar 

  10. He, W., Ge, S.S., How, B.V.E., Choo, Y.S., Hong, K.S.: Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica 47(4), 722–732 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. He, W., Zhang, S., Ge, S.S.: Adaptive control of a flexible crane system with the boundary output constraint. IEEE Trans. Ind. Electron. 61(8), 4126–4133 (2014)

    Article  Google Scholar 

  12. He, W., Zhang, S., Ge, S.S.: Robust adaptive control of a thruster assisted position mooring system. Automatica 50(7), 1843–1851 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sun, L., Huo, W., Jiao, Z.X.: Adaptive backstepping control of spacecraft rendezvous and proximity operations with input saturation and full state constraint. IEEE Trans. Ind. Electron. 64(1), 480–492 (2017)

    Article  Google Scholar 

  14. Kim, B.S., Yoo, S.J.: Approximation-based adaptive control of uncertain nonlinear pure-feedback systems with full state constraints. IET Control Theory Appl. 8(17), 2070–2081 (2014)

    Article  MathSciNet  Google Scholar 

  15. Liu, Y.J., Tong, S.C.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64(2), 70–75 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li J, Liu YJ (2015) Control of nonlinear systems with full state constraints using integral barrier Lyapunov functionals. In: International conference on informative and cybernetics for computational social systems, pp 66–71

  17. Li, D.J., Li, J., Li, S.: Adaptive control of nonlinear systems with full state constraints using integral barrier Lyapunov function. Neurocomputing 186, 90–96 (2016)

    Article  Google Scholar 

  18. Wang, C.X., Wu, Y.Q., Yu, J.B.: Barrier Lyapunov functions-based dynamic surface control for pure-feedback systems with full state constraints. IET Control Theory Appl. 11(4), 524–530 (2017)

    Article  MathSciNet  Google Scholar 

  19. He, W., Chen, Y.H., Yin, Z.: Adaptive neural network control of an uncertain robot with full state constraints. IEEE Trans. Cyber. 46(3), 620–629 (2016)

    Article  Google Scholar 

  20. Yue, H.Y., Li, J.M.: Output feedback adaptive fuzzy control for a class of nonlinear systems with input delay and unknown control directions. J. Franklin Inst. 350, 129–154 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, J., Chen, W.S., Li, J.M., Fang, Y.Q.: Adaptive NN output feedback stabilization for a class of stochastic nonlinear strict-feedback systems. ISA Trans. 48, 468–475 (2009)

    Article  Google Scholar 

  22. Chen, W.S., Li, J.M.: Decentralized output feedback neural control for systems with unknown interconnections. IEEE Trans. Syst. Man. Cybern. 38(1), 258–266 (2008)

    Article  MathSciNet  Google Scholar 

  23. K.P. Tee, S.S. Ge (2009) Control of nonlinear systems with full state constraint using a barrier Lyapunov function. In: IEEE conference on decision and control, pp 8618–8623

  24. Yin, Z., He, W., Yang, C.G.: Tracking control of a marine surface vessel with full state constraints. Int. J. Syst. Sci. 48(3), 535–546 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  25. Bai, R.: Neural network control-based adaptive design for a class of DC motor systems with the full state constraints. Neurocomputing 168, 65–69 (2015)

    Article  Google Scholar 

  26. Yin, Z., He, W., Ge, W.L.: Approximation-based control of a marine surface vessel with full state constraints. Intell. Robot. Appl. 9244, 111–125 (2015)

    Google Scholar 

  27. Liu, Y.J., Li, J., Tong, S.C.: Neural network control-based adaptive learning design for nonlinear systems with full state constraints. IEEE Trans. Neural Netw. Learn. Syst. 27(7), 1562–1571 (2016)

    Article  MathSciNet  Google Scholar 

  28. Kim, B.S., Yoo, S.J.: Approximation-based adaptive control of uncertain nonlinear pure-feedback systems with full state constraints. IET Control Theory Appl. 8(17), 2070–2081 (2014)

    Article  MathSciNet  Google Scholar 

  29. Liu, Y.J., Tong, S.C.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Gao, Y., Tong, S.C., Li, Y.M.: Adaptive fuzzy backstepping output feedback control for a class of uncertain stochastic nonlinear system in pure-feedback form. Neurocomputing 122, 126–133 (2013)

    Article  Google Scholar 

  31. Babuska, B., Schutter, B.D., Lendek Z, Guerra, TM.: Stability analysis and nonlinear observer design using Takagi-Sugeno fuzzy models. Studies in Fuzziness and Soft Computing. Springer, Berlin (2011)

  32. Li, Y.M., Tong, S.C.: Adaptive fuzzy output constrained control design for multi-input multioutput stochastic nonstrict-feedback nonlinear systems. IEEE Trans. Cybern. 47(12), 4086–4095 (2017)

    Article  Google Scholar 

  33. Liu, Y.J., Li, D.J., Tong, S.C.: Adaptive output feedback control for a class of nonlinear systems with full state constraints. Int. J. Control 87(2), 281–290 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Li, D.P., Li, D.J.: Adaptive neural tracking control for nonlinear time-delay systems with full state constraints. IEEE Trans. Syst. Man Cybern.: Syst. 47(7), 1590–1601 (2017)

    Article  Google Scholar 

  35. Chen, B., Zhang, H.G., Lin, C.: Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 89–98 (2016)

    Article  MathSciNet  Google Scholar 

  36. Wang, H.Q., Liu, K.F., Liu, X.P.: Neural-based adaptive output feedback control for a class of nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Cybern. 45(9), 1977–1987 (2015)

    Article  Google Scholar 

  37. Yu, Z.X., Li, S.G., Li, F.F.: Observer-based adaptive neural dynamic surface control for a class of nonstrict-feedback stochastic nonlinear systems. Int. J. Syst. Sci. 47(1), 194–208 (2016)

    Article  MATH  Google Scholar 

  38. Wu, J., Su, B.Y., Li, J.: Adaptive fuzzy control for full states constrained systems with nonstrict-feedback form and unknown nonlinear dead zone. Inf. Sci. 376, 233–247 (2017)

    Article  Google Scholar 

  39. Li, H., Bai, L., Wang, L., Zhou, Q., Wang, H.: Adaptive neural control of uncertain nonstrict-feedback stochastic nonlinear systems with output constraint and unknown dead zone. IEEE Trans. Syst. Man Cybern. Syst. 99, 1–12 (2016)

    Article  Google Scholar 

  40. Yao, B., Tomizuka, M.: Adaptive robust control of SISO nonlinear systems in a semi-strict-feedback form. Automatica 33(5), 893–900 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  41. Yao, B., Tomizuka, M.: Adaptive robust control of MIMO nonlinear systems in semi-strict-feedback forms. Automatica 37(9), 1305–1321 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang, H.Q., Liu, X.P., Liu, K.F.: Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. 23(5), 1746–1760 (2015)

    Article  Google Scholar 

  43. Yoo, S.J.: Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form. Int. J. Syst. Sci. 48(7), 1347–1355 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  44. Zhao, X.D., Yang, H.J., Karimi, H.R., Zhu, Y.Z.: Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time-delay. IEEE Trans. Cybern. 46(6), 1337–1349 (2016)

    Article  Google Scholar 

  45. Yang, H.J., Shi, P., Zhao, X.D., Shi, Y.: Adaptive output feedback neural tracking control for a class of nonstrict-feedback nonlinear systems. Inf. Sci. 334, 205–218 (2016)

    Article  Google Scholar 

  46. Li, Y.M., Tong, S.C.: Adaptive fuzzy output feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans. Cybern. 47(4), 1007–1016 (2017)

    Article  Google Scholar 

  47. Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for SISO uncertain nonstrict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)

    Article  Google Scholar 

  48. Li, Y.M., Tong, S.C., Liu, L., Feng, G.: Adaptive output feedback control design with prescribed performance for switched nonlinear systems. Automatica 80, 225–231 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  49. Sun, C.H.: Relaxed stabilization conditions for the T–S fuzzy system with input constraints. Int. J. Fuzzy Syst. 18(2), 168–176 (2016)

    Article  MathSciNet  Google Scholar 

  50. Tu, N.A.: Improved LMI conditions for local quadratic stabilization of constrained Takagi-Sugeno fuzzy systems. Int. J. Fuzzy Syst. 1, 1–13 (2016)

    Google Scholar 

  51. Hua, C., Wang, Q.G., Guan, X.P.: Adaptive fuzzy output feedback controller design for nonlinear time-delay systems with unknown control direction. IEEE Trans. Syst. Man Cybern. B Cybern. 39(2), 363–374 (2009)

    Article  Google Scholar 

  52. Yu, Z.X., Du, H.B.: Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: a Razumikhin functional method. Neurocomputing 74(12), 2072–2082 (2011)

    Article  Google Scholar 

  53. Chen, W.S., Jiao, L.C., Li, J., Li, R.H.: Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans. Syst. Man Cybern. B Cybern. 40(3), 939–950 (2010)

    Article  Google Scholar 

  54. Zhou, Q., Shi, P., Xu, S.Y., Li, H.Y.: Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans. Neural Netw. Learn. Syst. 24(1), 71–80 (2013)

    Article  Google Scholar 

  55. Li, Y., Tong, S.C., Li, Y.M.: “Observer-based adaptive fuzzy backstepping control for strict-feedback stochastic nonlinear systems with time delays. Int. J. Innov. Comput. Inf. Control 8(12), 8103–8114 (2012)

    Google Scholar 

  56. Su, X.J., Shi, P., Wu, L., Song, Y.D.: A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. 21(4), 655–671 (2013)

    Article  Google Scholar 

  57. Wang, M., Chen, B., Liu, X., Shi, P.: Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets Syst. 159(8), 949–967 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  58. Hua, C.C., Guan, X.P., Shi, P.: Robust backsteping control for a class of time delayed systems. IEEE Trans. Autom. Control 50(6), 894–899 (2005)

    Article  MATH  Google Scholar 

  59. Daniel, W., Li, J.M., Niu, Y.G.: Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Trans. Neural Netw. 16(3), 625–635 (2005)

    Article  Google Scholar 

  60. Li, J.M., Yue, H.Y.: Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time-varying delay. Int. J. Adapt. Control Signal Process. 29, 614–638 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  61. Li, J.M., Yue, H.Y.: Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays. Appl. Math. Comput. 256, 514–528 (2015)

    MathSciNet  MATH  Google Scholar 

  62. Hua, C.C., Guan, X.P., Shi, P.: Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Trans. Neural Netw. 18(2), 495–505 (2007)

    Article  Google Scholar 

  63. Chen, B., Lin, C., Liu, X.P.: Observer-based adaptive fuzzy control for a class of nonlinear delayed systems. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 27–36 (2016)

    Article  Google Scholar 

  64. Zhou, Q., Shi, P., Xu, S.Y., Li, H.Y.: Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 21(22), 301–313 (2013)

    Article  Google Scholar 

  65. Zhang, T.P., Ge, S.S.: Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions. IEEE Trans. Neural Netw. 20(3), 483–497 (2009)

    Article  Google Scholar 

  66. Chen, B., Liu, X.P., Liu, K.F.: Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE Trans. Fuzzy Syst. 22(2), 237–248 (2014)

    Article  Google Scholar 

  67. Zhai, D., Xi, C.J., Dong, J.X., Zhang, Q.L.: Delay-estimation-based adaptive fuzzy memory control for a class of uncertain nonlinear time-delay systems. Fuzzy Sets Syst. 316, 1–19 (2017)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported in part by National Nature Science Foundation of China under Grant 61573013, 61673014.

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Jiale Yi, Junmin Li & Jing Li

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  1. Jiale Yi
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  2. Junmin Li
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Correspondence to Junmin Li.

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Yi, J., Li, J. & Li, J. Adaptive Fuzzy Output Feedback Control for Nonlinear Nonstrict-Feedback Time-Delay Systems with Full State Constraints. Int. J. Fuzzy Syst. 20, 1730–1744 (2018). https://doi.org/10.1007/s40815-018-0475-6

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