Advertisement

International Journal of Fuzzy Systems

, Volume 18, Issue 6, pp 990–998 | Cite as

Composite Learning Fuzzy Control of Uncertain Nonlinear Systems

  • Yongping Pan
  • Meng Joo Er
  • Yiqi Liu
  • Lin Pan
  • Haoyong YuEmail author
Article

Abstract

Function approximation accuracy and computational cost are two major concerns in approximation-based adaptive fuzzy control. In this paper, a model reference composite learning fuzzy control strategy is proposed for a class of affine nonlinear systems with functional uncertainties. In the proposed approach, a modified modeling error that utilizes data recorded online is defined as a prediction error, a linear filter is applied to estimate time derivatives of plant states, and both the tracking error and the prediction error are exploited to update parametric estimates. It is proven that the closed-loop system achieves semiglobal practical exponential stability by an interval-excitation condition which is much weaker than a persistent-excitation condition. Compared with a concurrent learning approach that has the same aim as this study, the computational cost of the proposed approach is significantly reduced for the guarantee of accurate function approximation. An illustrative example of aircraft wing rock control has been provided to verify effectiveness of the proposed control strategy.

Keywords

Adaptive control Fuzzy approximation Composite learning Interval excitation Parameter convergence Online modeling 

Notes

Acknowledgments

This work was supported in part by the Future System Directorate, Ministry of Defence, Singapore under Grant No. MINDEF-NUS-DIRP/2012/02, and in part by the Ministry of Education, Singapore (Tier 1 AcRF, RG29/15).

References

  1. 1.
    Wang, L.X.: A Course in Fuzzy Systems and Fuzzy Control. Prentice Hall, Englewood Cliffs (1997)zbMATHGoogle Scholar
  2. 2.
    Chang, Y.H., Chan, W.S., Chang, C.W., Tao, C.W.: Adaptive fuzzy dynamic surface control for ball and beam system. Int. J. Fuzzy Syst. 13(1), 1–7 (2011)MathSciNetGoogle Scholar
  3. 3.
    Pan, Y.P., Er, M.J., Huang, D.P., Wang, Q.R.: Adaptive fuzzy control with guaranteed convergence of optimal approximation error. IEEE Trans. Fuzzy Syst. 19(5), 807–818 (2011)CrossRefGoogle Scholar
  4. 4.
    Pan, Y.P., Er, M.J., Huang, D.P., Sun, T.R.: Practical adaptive fuzzy H tracking control of uncertain nonlinear systems. Int. J. Fuzzy Syst. 14(4), 463–473 (2012)MathSciNetGoogle Scholar
  5. 5.
    Precup, R.E., David, R.C., Petriu, E.M., Preitl, S., Radac, M.B.: Fuzzy logic-based adaptive gravitational search algorithm for optimal tuning of fuzzy-controlled servo systems. IET Control Theory Appl. 7(1), 99–107 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Yousef, H.A., Hamdy, M., Shafiq, M.: Flatness-based adaptive fuzzy output tracking excitation control for power system generators. J. Frankl. Inst. 350(8), 2334–2353 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Lee, C.H., Hsueh, H.Y.: Observer-based adaptive control for a class of nonlinear non-affine systems using recurrent-type fuzzy logic systems. Int. J. Fuzzy Syst. 15(1), 55–65 (2013)MathSciNetGoogle Scholar
  8. 8.
    Lin, H.W., Chan, W.S., Chang, C.W., Yang, C.Y., Chang, Y.H.: Adaptive neuro-fuzzy formation control for leader–follower mobile robots. Int. J. Fuzzy Syst. 15(3), 359–370 (2013)MathSciNetGoogle Scholar
  9. 9.
    Pan, Y.P., Er, M.J.: Enhanced adaptive fuzzy control with optimal approximation error convergence. IEEE Trans. Fuzzy Syst. 21(6), 1123–1132 (2013)CrossRefGoogle Scholar
  10. 10.
    Hamdy, M., Hamdan, I.: Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark. ISA Trans. 57, 85–92 (2015)CrossRefGoogle Scholar
  11. 11.
    Li, Y.M., Tong, S.C., Li, T.S.: Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control direction and unknown dead-zones. IEEE Trans. Fuzzy Syst. 23(4), 1228–1241 (2015)CrossRefGoogle Scholar
  12. 12.
    Chowdhary, G.V., Muhlegg, M., Johnson, E.N.: Exponential parameter and tracking error convergence guarantees for adaptive controllers without persistency of excitation. Int. J. Control 87(8), 1583–1603 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Slotine, J.-J.E., Li, W.: Composite adaptive control of robot manipulators. Automatica 25(4), 509–519 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Golea, N., Golea, A., Benmahammed, K.: Fuzzy model reference adaptive control. IEEE Trans. Fuzzy Syst. 10(4), 436–444 (2002)zbMATHCrossRefGoogle Scholar
  15. 15.
    Hojati, M., Gazor, S.: Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans. Fuzzy Syst. 10(2), 198–210 (2002)CrossRefGoogle Scholar
  16. 16.
    Nakanishi, J., Farrell, J.A., Schaal, S.: Composite adaptive control with locally weighted statistical learning. Neural Netw. 18(1), 71–90 (2005)zbMATHCrossRefGoogle Scholar
  17. 17.
    Nounou, H.N., Passino, K.M.: Stable auto-tuning of hybrid adaptive fuzzy/neural controllers for nonlinear systems. Eng. Appl. Artif. Intell. 18(3), 317–334 (2005)CrossRefGoogle Scholar
  18. 18.
    Bellomo, D., Naso, D., Babuska, R.: Adaptive fuzzy control of a non-linear servo-drive: theory and experimental results. Eng. Appl. Artif. Intell. 21(6), 846–857 (2008)CrossRefGoogle Scholar
  19. 19.
    Naso, D., Cupertino, F., Turchiano, B.: Precise position control of tubular linear motors with neural networks and composite learning. Control Eng. Pract. 18(5), 515–522 (2010)CrossRefGoogle Scholar
  20. 20.
    Patre, P.M., Bhasin, S., Wilcox, Z.D., Dixon, W.E.: Composite adaptation for neural network-based controllers. IEEE Trans. Autom. Control 55(4), 944–950 (2010)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Pan, Y.P., Er, M.J., Sun, T.R.: Composite adaptive fuzzy control for synchronizing generalized Lorenz systems. Chaos 22(2), 023144 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Pan, Y.P., Zhou, Y., Sun, T.R., Er, M.J.: Composite adaptive fuzzy H tracking control of uncertain nonlinear systems. Neurocomputing 99, 15–24 (2013)CrossRefGoogle Scholar
  23. 23.
    Huang, Y.S., Liu, W.P., Wu, M., Wang, Z.W.: Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS. ISA Trans. 53(5), 1569–1581 (2014)CrossRefGoogle Scholar
  24. 24.
    Xu, B., Shi, Z., Yang, C.: Composite fuzzy control of a class of uncertain nonlinear systems with disturbance observer. Nonlinear Dyn. 80(1), 341–351 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Li, Y.M., Tong, S.C., Li, T.S.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2015)CrossRefGoogle Scholar
  26. 26.
    Pan, Y.P., Sun, T.R., Pan, L., Yu, H.Y.: Robustness analysis of composite adaptive robot control. In: Proceedings Chinese Control Decision Conference, pp. 1–6. Yinchuang (2016)Google Scholar
  27. 27.
    Xu, B., Sun, F.C., Pan, Y. P., Chen, B. D.:Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE Trans. Syst. Man Cybern.: Syst. (2016). doi: 10.1109/TSMC.2016.2562502
  28. 28.
    Li, Y.M., Tong, S.C., Li, T.S.: Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation. IEEE Trans. Fuzzy Syst. (2015). doi: 10.1109/TFUZZ.2015.2486811
  29. 29.
    Pan, Y.P., Pan, L., Yu, H.Y.: Composite learning control with application to inverted pendulums. In: Proceedings Chinese Automation Congress, pp. 232–236. Wuhan (2015)Google Scholar
  30. 30.
    Pan, Y.P., Pan, L., Darouach, M., Yu, H.Y.: Composite learning: An efficient way of parameter estimation in adaptive control. In: Proceedings Chinese Control Conference, pp. 1–6. Chengdu (2016)Google Scholar
  31. 31.
    Pan, Y.P., Sun, T.R., Yu, H.Y.: Biomimetic composite learning for robot motion control. In: Proceedings IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 1–6. Singapore (2016)Google Scholar
  32. 32.
    Pan, Y.P., Yu, H.Y.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control. (2015). doi: 10.1109/TAC.2015.2495232
  33. 33.
    Pan, Y.P., Zhang, J., Yu, H.Y.: Model reference composite learning control without persistency of excitation. IET Control Theory Appl. (2016). doi: 10.1049/iet-cta.2016.0032
  34. 34.
    Pan, Y.P., Er, M.J., Pan, L., Yu, H.Y.: Composite learning from model reference adaptive fuzzy control. In: Proceedings International Conference on Fuzzy Set Theory and Applications, pp. 91–96. Yilan (2015)Google Scholar
  35. 35.
    Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice Hall, Englewood Cliffs (1996)zbMATHGoogle Scholar
  36. 36.
    Pan, Y.P., Yu, H.Y.: Dynamic surface control via singular perturbation analysis. Automatica 51, 29–33 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Hu, J.C., Zhang, H.H.: Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles. Automatica 49(7), 2160–2167 (2013)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Dong, W.J., Farrell, J.A., Polycarpou, M.M., Djapic, V., Sharma, M.: Command filtered adaptive backstepping. IEEE Trans. Control Syst. Technol. 20(3), 566–580 (2012)CrossRefGoogle Scholar
  39. 39.
    Khalil, H.K.: Nonlinear Control. Prentice Hall, Upper Saddle River (2015)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yongping Pan
    • 1
  • Meng Joo Er
    • 2
  • Yiqi Liu
    • 3
  • Lin Pan
    • 4
  • Haoyong Yu
    • 1
    Email author
  1. 1.Department of Biomedical EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina
  4. 4.School of Logistics EngineeringWuhan University of TechnologyWuhanChina

Personalised recommendations