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Fuzzy neural adaptive tracking control of unknown chaotic systems with input saturation

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Abstract

The contribution of this work is to study the control of unknown chaotic systems with input saturation, and the backstepping-based an adaptive fuzzy neural controller (AFNC) is proposed. In many practical dynamic systems, physical input saturation on hardware dictates that the magnitude of the control signal is always constrained. Saturation is a potential problem for actuators of control systems. It often severely limits system performance, giving rise to undesirable inaccuracy or leading instability. To deal with saturation, we construct a new system with the same order as that of the plant. With the error between the control input and saturation input as the input of the constructed system, a number of signals are generated to compensate the effect of saturation. Finally, simulation results show that the AFNC can achieve favorable tracking performances.

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References

  1. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Raj, S.P., Rajasekar, S.: Migration control in two couple Duffing oscillators. Phys. Rev. E 55, 6237–6240 (1997)

    Article  Google Scholar 

  3. Myneni, K., Barr, T.: New method for the control of fast chaotic oscillations. Phys. Rev. Lett. 83, 2175–2178 (1999)

    Article  Google Scholar 

  4. Yu, Y., Zhang, S.: Controlling uncertain Lü system using backstepping design. Chaos Solitons Fractals 15, 897–902 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hua, C., Guan, X., Shi, P.: Adaptive feedback control for a class of chaotic systems. Chaos Solitons Fractals 23, 757–765 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Soong, C.Y., Huang, W.T., Lin, F.P.: Chaos control on autonomous and non-autonomous systems with various types of genetic algorithm-optimized weak perturbations. Chaos Solitons Fractals 34, 1519–1537 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57, 431–439 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, H.G., Li, M., Yang, J., Yang, D.D.: Fuzzy model-based robust networked control for a class of nonlinear systems. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 39, 437–447 (2009)

    Article  Google Scholar 

  9. Tong, S.C., Li, Y.M.: Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160, 1749–1764 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tong, S.C., Li, C.Y., Li, Y.M.: Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160, 2755–2775 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177, 3901–3917 (2007)

    Article  MATH  Google Scholar 

  12. Liu, Y.J., Tong, S.C., Wang, W.: Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst. 160, 2727–2754 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, Y.J., Tong, S.C., Wang, W., Li, Y.M.: Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications. Int. J. Control. Autom. Syst. 7, 681–690 (2009)

    Article  Google Scholar 

  14. Zhou, N., Liu, Y.J., Tong, S.C.: Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input. Nonlinear Dyn. 63, 771–778 (2011)

    Article  MathSciNet  Google Scholar 

  15. Liu, Y.J., Tong, S.C., Li, T.S.: Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst. 164, 25–44 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1, 4–27 (1990)

    Article  Google Scholar 

  17. Hunt, K.J., Sbarbaro, D., Zbikowski, R., Gawthrop, P.J.: Neural networks for control: a survey. Automatica 28, 1083–1112 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22, 1162–1167 (2011)

    Article  Google Scholar 

  19. Liu, Y.J., Tong, S.C., Wang, D., Li, T.S., Chen, C.L.P.: Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear siso systems. IEEE Trans. Neural Netw. (2011). doi:10.1109/TNN.2011.2159865

  20. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  21. Yu, W., Li, X.: Fuzzy identification using fuzzy neural networks with stable learning algorithms. IEEE Trans. Fuzzy Syst. 12, 411–420 (2004)

    Article  Google Scholar 

  22. Jang, J.S.: ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23, 665–685 (1993)

    Article  Google Scholar 

  23. Lin, C.T., Lee, C.S.G.: Neural Fuzzy Systems. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  24. Chen, B., Liu, X., Tong, S.: Adaptive fuzzy approach to control unified chaotic systems. Chaos Solitons Fractals 34, 1180–1187 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kim, J.H., Hyun, C.H., Kim, E., Park, M.: Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15, 359–369 (2007)

    Article  Google Scholar 

  26. Wang, X., Meng, J.: Observer-based adaptive fuzzy synchronization for hyperchaotic systems. Chaos 18, 033102-5 (2008)

    MathSciNet  Google Scholar 

  27. Roopaei, M., Jahromi, M.Z., Jafari, S.: Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros. Chaos 19, 013125-9 (2009)

    Article  Google Scholar 

  28. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40, 170–184 (2010)

    Article  Google Scholar 

  29. Lin, D., Wang, X.: Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation. Fuzzy Sets Syst. 161, 2066–2080 (2010)

    Article  MATH  Google Scholar 

  30. Kapoor, N., Teel, A.R., Daoutidis, P.: An anti-windup design for linear systems with input saturation. Automatica 34, 559–574 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  31. Bemporad, A., Teel, A.R., Zaccarian, L.: Anti-windup synthesis via sampled-data piecewise affine optimal control. Automatica 40, 549–562 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Fliegner, T., Logemann, H., Ryan, E.P.: Low-gain integral control of continuous time linear systems subject to input and output nonlinearities. Automatica 39, 455–462 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Grognard, F., Sepulchre, R., Bastin, G.: Improving the performance of low-gain designs for bounded control of linear systems. Automatica 38, 1777–1782 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chaoui, F.Z., Giri, F., Msaad, M.: Asymptotic stabilization of linear plants in the presence of input and output saturations. Automatica 37, 37–42 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  35. Karason, S.P., Annaswamy, A.M.: Adaptive control in the presence of input constraints. IEEE Trans. Autom. Control 39, 2325–2330 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  36. Nicolao, G.D., Scattolini, R., Sala, G.: An adaptive predictive regulator with input saturations. Automatica 32, 597–601 (1996)

    Article  MATH  Google Scholar 

  37. Chaoui, F.Z., Giri, F., Msaad, M.: Adaotive control of input-constrained tyoe-1 plants stabilization and tracking. Automatica 37, 197–203 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  38. Jagannathan, S., Hameed, M.: Adaptive force-banlancing control of MEMS gyroscope with actuator limits. In: Proceedings of American Control Conference, Boston, Massachusetts, pp. 1862–1867 (2004)

    Google Scholar 

  39. Zhou, J., Wen, C.: Adaptive backstepping control of uncertain systems. In: LNCS, vol. 372, pp. 189–197. Springer, Berlin (2008)

    Google Scholar 

  40. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)

    Google Scholar 

  41. Jamshidi, M., Vadiee, N., Ress, T.J.: Fuzzy Logic and Control. Prentice-Hall, Englewood Cliffs (1993)

    Google Scholar 

  42. Leu, Y.G., Lee, T.T., Wang, W.Y.: On-line tuning of fuzzy-neural network for adaptive control of nonlinear dynamical systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 27, 1034–1043 (1997)

    Article  Google Scholar 

  43. Lin, C.T., Lee, C.S.G.: Neural-network-based fuzzy logic control and decision system. IEEE Trans. Comput. 40, 1320–1336 (1991)

    Article  MathSciNet  Google Scholar 

  44. Chen, Y.C., Teng, C.C.: A model reference control structure using a fuzzy neural network. Fuzzy Sets Syst. 73, 291–312 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1, 146–155 (1993)

    Article  Google Scholar 

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Correspondence to Da Lin.

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Lin, D., Wang, X. & Yao, Y. Fuzzy neural adaptive tracking control of unknown chaotic systems with input saturation. Nonlinear Dyn 67, 2889–2897 (2012). https://doi.org/10.1007/s11071-011-0196-y

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