Abstract
This paper proposes a wavelet-based cerebellar model arithmetic controller neural network (called WCMAC) and develops an adaptive supervisory WCMAC control (SWC) scheme for nonlinear uncertain systems. The WCMAC is modified from the traditional CMAC for obtaining high approximation accuracy and convergent rate using the advantages of wavelet functions and fuzzy TSK-model. For nonlinear uncertain systems, a PD-type WCMAC controller with filter is constructed to approximate an ideal control signal. The corresponding adaptive supervisory controller is used to recover the residual of approximation error. Finally, the adaptive SWC scheme is applied to chaotic system identification and control including Mackey–Glass time-series prediction, control of inverted pendulum system, and control of Chua circuit system. These demonstrate the effectiveness of our adaptive SWC approach for nonlinear uncertain systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albus JS (1975a) A new approach to manipulator control: the cerebellar model articulation controller (CMAC). ASME J Dyn Syst Meas Control 97: 220–227
Albus JS (1975b) Data storage in the cerebellar model articulation controller (CMAC). ASME J Dyn Syst Meas Control 97: 228–233
Almeida PEM, Simoes MG (2005) Neural optimal control of PEM fuel cells with parametric CMAC networks. IEEE Trans Ind Appl 41(1): 237–245
Banakar A, Azeem MF (2007) Artificial wavelet neuro-fuzzy model based on parallel wavelet network and neural network, soft computing (in press). doi:10.1007/s00500-007-0238-z
Casdagli M (1992) A dynamical systems approach to modeling input-output systems. In: Nonlinear modeling and forecasting, SFI studies in the sciences of complexity process, vol 12. Addison-Wesley, New York, pp 265–281
Chatterjee A, Watanabe K (2005) An adaptive fuzzy strategy for motion control of robot manipulators. Soft Comput 9(3): 185–193
Chen G, Dong X (1993) On feedback control of chaotic continuous-time systems. IEEE Trans Circuits Syst I Fundam Theory Appl 4(9)
Commuri S, Lewis FL (1997) CMAC neural networks for control nonlinear dynamical systems: structure, stability, and passivity. Automatica 33(4): 635–641
Frayman Y, Wang L (2002) A dynamically-constructed fuzzy neural controller for direct model reference adaptive control of multi-input-multi-output nonlinear processes. Soft Comput 6(3): 244–253
Gan Q, Rosales E (2003) CMAC for local linear modeling and regularization techniques for improving local linearity approximation. In: Proc. of the UK workshop on computational intelligence (UKCI2003), Bristol, UK, pp 131–138
Glanz FH, Miller WT, Kraft LG (1991) An overview of the CMAC neural network. In: Proc. 1991 IEEE neural networks ocean eng., pp 301–308
Hu J, Pratt J, Pratt G (1999) Stable adaptive control of a bipedal walking; robot with CMAC neural networks. In: Proc. 1999 IEEE Int. Conf. Robot. Automat., vol 2, pp 1050–1056
Jagannthan S, Commuri S, Lewis FL (1998) Feedback linearization using CMAC neural networks. Automatica 34(5): 547–557
Lee CH (2004) Stabilization of nonlinear nonminimum phase systems: an adaptive parallel approach. IEEE Trans Syst Man Cybern Part B 34(2): 1075–1088
Lee CH, Lin YC (2005) An adaptive type-2 fuzzy neural controller for nonlinear uncertain systems. Int J Control Intell Syst 12(1): 41–50
Lee CH, Teng CC (2000) Identification and control of dynamic systems using recurrent fuzzy neural networks. IEEE Trans Fuzzy Syst 8(4): 349–366
Lee CH, Wang BH (2007) Adaptive wavelet-based-CMAC network predictor design for lossless image coding. Eng Lett 15(1): 119–125
Lee ZJ, Wang YP, Su SF (2004) A genetic algorithm based Robust learning credit assignment cerebellar model articulation controller. Appl Soft Comput 4(4): 357–367
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
Lin CT, Lee CSG (1996) Neural fuzzy systems. Prentice Hall, Englewood Cliff
Lin CJ, Xu YJ (2006) A novel evolution learning for recurrent wavelet-based neuro-fuzzy networks. Soft Comput 10(3): 193–205
Lin CJ, Chen HJ, Lee CY (2004) A self-organizing recurrent fuzzy CMAC model for dynamic system identification. In: 2004 IEEE int. conf. on fuzzy systems, pp 697–702
Lin FJ, Wai RJ, Huang PK (2004) Two-axis motion control system using wavelet neural network for ultrasonic motor drives. IEEE Proc Electr Power Appl 151(5): 613–621
Ling SH, Leung FHF, Lam HK (2007) Input-dependent neural network trained by real-coded genetic algorithm and its industrial applications. Soft Comput 11(11): 1033–1052
Liu J, Liu D, Bai HY, Wu PS, Han X (2006) A new strategy for optimizing the parameters updating algorithm of fuzzy neural controller. Soft Comput 10(1): 61–67
Lo SCB, Li H, Freedman MT (2003) Optimization of wavelet decomposition for image compression and feature preservation. IEEE Trans Med Imaging 22(9): 1141–1151
Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197: 287–289
Mantas CJ (2008) A generic fuzzy aggregation operator: rules extraction from and insertion into artificial neural networks. Soft Comput 12(5): 493–514
Miller WT, Glanz FH, Kraft LG (1990) CMAC: an associative neural network alternative to backpropagation. Proc IEEE 78: 1561–1567
Nunnari G (2004) Modelling air pollution time-series by using wavelet functions and genetic algorithms. Soft Comput 8(3): 173–178
Peng YF, Wai RJ, Lin CM (2004) Implementation of LLCC-resonant driving circuit and adaptive CMAC neural network control for linear piezoelectric ceramic motor. IEEE Trans Ind Electron 51(1): 35–48
Slotine JJE, Li W (1991) Applied nonlinear control. Prentice-Hall, Upper Saddle River
Wai RJ, Lin CM, Peng YF (2004) Adaptive hybrid control for linear piezoelectric ceramic motor drive using diagonal recurrent CMAC network. IEEE Trans Neural Netw 15(6): 1491–1506
Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Upper Saddle River
Wang S, Lu H (2003) Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators. Soft Comput 7(8): 566–573
Wang CH, Lin TC, Lee TT, Liu HL (2002) Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems. IEEE Trans Syst Man Cybern B 32: 583–597
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, CH., Wang, BH. Adaptive supervisory WCMAC neural network controller (SWC) for nonlinear systems. Soft Comput 13, 1–12 (2009). https://doi.org/10.1007/s00500-008-0287-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-008-0287-y