Abstract
Recurrent wavelet neural network (RWNN) has the advantages in its dynamic responses and information storing ability. This paper develops a recurrent wavelet neural backstepping control (RWNBC) scheme for multiple-input multiple-output (MIMO) mechanical systems. This proposed RWNBC comprises a neural controller and a smooth compensator. The neural controller using an RWNN is the principal tracking controller utilized to mimic an ideal backstepping control law; and the parameters of RWNN are online tuned by the derived adaptation laws from the Lyapunov stability theorem. The smooth compensator is designed to dispel the approximation error introduced by the neural controller, so that the asymptotic stability of the closed-loop system can be guaranteed. Finally, two MIMO mechanical systems, a mass-spring-damper system and a two-inverted pendulum system, are performed to verify the effectiveness of the proposed RWNBC scheme. From the simulation results, it is verified that the proposed RWNBC scheme can achieve favorable tracking performance without any chattering phenomenon.
Similar content being viewed by others
References
Lin CM, Hsu CF (2003) Neural network hybrid control for antilock braking systems. IEEE Trans Neural Netw 14(2):351–359
Park JH, Huh SH, Kim SH, Seo SJ, Park GT (2005) Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks. IEEE Trans Neural Netw 16(2):414–422
Hsu CF (2007) Self-organizing adaptive fuzzy neural control for a class of nonlinear systems. IEEE Trans Neural Netw 18(4):1232–1241
Da F (2007) Fuzzy neural network sliding mode control for long delay time systems based on fuzzy prediction. Neural Comput Appl 17(5):531–539
Wang Z, Zhang Y, Fang H (2008) Neural adaptive control for a class of nonlinear systems with unknown deadzone. Neural Comput Appl 17(4):339–345
Lin CM, Hsu CF (2004) Supervisory recurrent fuzzy neural network control of wing rock for slender delta wings. IEEE Trans Fuzzy Syst 12(5):733–742
Zhai JY, Fei SM, Mo XH (2008) Multiple models switching control based on recurrent neural networks. Neural Comput Appl 17(4):365–371
Hsu CF (2009) Adaptive recurrent neural network control using a structure adaptation algorithm. Neural Comput Appl 18(2):115–125
Hsu CF (2009) Intelligent position tracking control for LCM drive using stable online self-constructing recurrent neural network controller with bound architecture. Control Engineering Practice 17(6):714–722
Zhang Q (1997) Using wavelet network in nonparametric estimation. IEEE Trans Neural Netw 8(2):227–236
Wai RJ (2002) Development of new training algorithms for neuro-wavelet systems on the robust control of induction servo motor drive. IEEE Trans Ind Electron 49(6):1323–1341
Hsu CF, Lin CM, Lee TT (2006) Wavelet adaptive backstepping control for a class of nonlinear systems. IEEE Trans Neural Netw 17(5):1175–1183
Hsu CF, Cheng KH, Lee TT (2009) Robust wavelet-based adaptive neural controller design with a fuzzy compensator. Neurocomputing 73(1):423–431
Zhang T, Ge SS, Hang CC (2000) Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12):1835–1846
Hsu CF, Lin CM (2005) Fuzzy-identification-based adaptive controller design via backstepping approach. Fuzzy Syst 151(1):43–57
Chen PC, Hsu CF, Lee TT, Wang CH (2009) Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system. Soft Comput 13(7):635–647
Lin CM, Hsu CF (2002) Neural-network-based adaptive control for induction servomotor drive system. IEEE Trans Ind Electron 49(1):115–123
Chang YC (2004) Robust H ∞ control for a class of uncertain nonlinear time-varying systems and its application. IEE Proc Control Theory Appl 151(5):601–609
Chang YC, Yen HM (2005) Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks. IEEE Trans Syst Man Cybern B Cybern 35(6):1311–1316
Salim L, Mohamed SB, Thierry MG (2005) Adaptive fuzzy control of a class of MIMO nonlinear systems. Fuzzy Sets and Syst 151(1):59–77
Tong S, Chen B, Wang Y (2005) Fuzzy adaptive output feedback control for MIMO nonlinear systems. Fuzzy Sets and Syst 156(2):285–299
Slotine JJE, Li WP (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs
Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs
Lin CM, Chen LY, Chen CH (2007) RCMAC hybrid control for MIMO uncertain nonlinear systems using sliding-mode technology. IEEE Trans Neural Netw 18(3):708–720
Zhou S, Feng G, Feng CB (2005) Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping. Fuzzy Sets Syst 151(1):1–20
Acknowledgments
The authors appreciate the partial financial support from the National Science Council of Republic of China under grant NSC 98-2218-E-163-002.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, CH., Hsu, CF. Recurrent wavelet neural backstepping controller design with a smooth compensator. Neural Comput & Applic 19, 1089–1100 (2010). https://doi.org/10.1007/s00521-010-0347-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-010-0347-y