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.
Notes
The special definition is based on a consideration that \(\Theta (t_e) W^*\) is not computable by (11) due to the unmeasurable \(\dot{e}_n\).
References
Wang, L.X.: A Course in Fuzzy Systems and Fuzzy Control. Prentice Hall, Englewood Cliffs (1997)
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)
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)
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)
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)
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)
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)
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)
Pan, Y.P., Er, M.J.: Enhanced adaptive fuzzy control with optimal approximation error convergence. IEEE Trans. Fuzzy Syst. 21(6), 1123–1132 (2013)
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)
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)
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)
Slotine, J.-J.E., Li, W.: Composite adaptive control of robot manipulators. Automatica 25(4), 509–519 (1989)
Golea, N., Golea, A., Benmahammed, K.: Fuzzy model reference adaptive control. IEEE Trans. Fuzzy Syst. 10(4), 436–444 (2002)
Hojati, M., Gazor, S.: Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans. Fuzzy Syst. 10(2), 198–210 (2002)
Nakanishi, J., Farrell, J.A., Schaal, S.: Composite adaptive control with locally weighted statistical learning. Neural Netw. 18(1), 71–90 (2005)
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)
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)
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)
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)
Pan, Y.P., Er, M.J., Sun, T.R.: Composite adaptive fuzzy control for synchronizing generalized Lorenz systems. Chaos 22(2), 023144 (2012)
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)
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)
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)
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)
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)
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
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
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)
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)
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)
Pan, Y.P., Yu, H.Y.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control. (2015). doi:10.1109/TAC.2015.2495232
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
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)
Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice Hall, Englewood Cliffs (1996)
Pan, Y.P., Yu, H.Y.: Dynamic surface control via singular perturbation analysis. Automatica 51, 29–33 (2015)
Hu, J.C., Zhang, H.H.: Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles. Automatica 49(7), 2160–2167 (2013)
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)
Khalil, H.K.: Nonlinear Control. Prentice Hall, Upper Saddle River (2015)
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).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pan, Y., Er, M.J., Liu, Y. et al. Composite Learning Fuzzy Control of Uncertain Nonlinear Systems. Int. J. Fuzzy Syst. 18, 990–998 (2016). https://doi.org/10.1007/s40815-016-0243-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-016-0243-4