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Hierarchical fuzzy CMAC control for nonlinear systems

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Abstract

In this study, a novel indirect adaptive controller is introduced for a class of unknown nonlinear systems. The proposed method provides a simple control architecture that merges from the cerebellar model articulation controller (CMAC) network and hierarchical fuzzy logic; therefore, the complicated CMAC structure can be simplified. The overall adaptive scheme guarantees the uniform stability of the closed-loop system. A simulation is presented to demonstrate the performance of the proposed methodology.

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References

  1. Aguilar-Ibañez CF (2009) The Lyapunov direct method for the stabilization of the ball on the actuated beam. Int J Control 82(12):2169–2178

    Article  MATH  Google Scholar 

  2. Aguilar-Ibañez CF, Garrido Moctezuma R, Davila J (2012) Output feedback trajectory stabilization of the uncertainty DC servomechanism system. ISA Trans 51(6):801–807

    Article  Google Scholar 

  3. Angelov P, Kordon A (2010) Adaptive inferential sensors based on evolving fuzzy models. IEEE Trans Syst Man Cybern B Cybern 40(2):529–539

    Article  Google Scholar 

  4. Angelov P (2011) Fuzzily connected multimodel systems evolving autonomously from data streams. IEEE Trans Syst Man Cybern B Cybern 41(4):898–910

    Article  Google Scholar 

  5. Albus JS (1975) A New approach to manipulator control: the cerebellar model articulation controller (CMAC). J Dyn Syst Meas Control Trans ASME 97:220–227

    Google Scholar 

  6. Chen C-T (1998) Linear system theory and design, 3rd edn. Oxford University Press, Oxford, ISBN 0-19-511777-8

  7. Chen C-H (2012) Wavelet-based adaptive robust control for a class of MIMO uncertain nonlinear systems. Neural Comput Appl 21:747–762

    Article  Google Scholar 

  8. Chen C-S (2011) Supervisory adaptive tracking control of robot manipulators using interval type-2 TSK fuzzy logic system. IET Control Theory Appl 5(15):1796–1807

    Article  MathSciNet  Google Scholar 

  9. Fan X, Zhang N, Teng S (2003) Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme. Fuzzy Sets Syst 144:297–312

    Article  MathSciNet  MATH  Google Scholar 

  10. Fan L-L, Song Y-D (2012) Neuro-adaptive model-reference fault-tolerant control with application to wind turbines. IET Control Theory Appl 6(4):475–486

    Article  MathSciNet  Google Scholar 

  11. Han SI, Lee JM (2011) Friction and uncertainty compensation of robot manipulator using optimal recurrent cerebellar model articulation controller and elasto-plastic friction observer. IET Control Theory Appl 5(18):2120–2141

    Article  MathSciNet  Google Scholar 

  12. Hojati M, Gazor S (2002) Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans Fuzzy Syst 10(2):198–210

    Google Scholar 

  13. Isidori A (1999) Nonlinear control systems II. Springer, Berlin, ISBN 1-85233-188-7

  14. Jimenez-Lizarraga M, Basin M, Rodriguez-Ramirez P (2012) Robust mini–max regulator for uncertain non-linear polynomial systems. IET Control Theory Appl 6(7):963–970

    Article  MathSciNet  Google Scholar 

  15. Jimenez-Lizarraga M, Basin M, Rodriguez-Ramirez P, Rubio JJ (2012) Robust control of a nonlinear electrical oscillator modeled by buffing equation. Int J Innov Comput Inf Control 8(5(A)):2941–2952

    Google Scholar 

  16. Jiménez-Lizárraga M, Poznyak A (2012) Necessary conditions for Robust Stackelberg equilibrium in a multi-model differential game. Optim Control Appl Methods 33(5):595–613

    Article  MathSciNet  MATH  Google Scholar 

  17. Knuplez A, Chowdhury A, Svecko R (2003) Modeling and control design for the ball and plate system. IEEE Int Conf Indus Technol 2:1064–1067

    Google Scholar 

  18. Leite D, Ballini R, Costa P, Gomide F (2012) Evolving fuzzy granular modeling from nonstationary fuzzy data streams. Evol Syst 3(2):65–79

    Article  Google Scholar 

  19. Lemos A, Caminhas W, Gomide F (2011) Multivariable Gaussian evolving fuzzy modeling system. IEEE Trans Fuzzy Syst 19(1):91–104

    Article  Google Scholar 

  20. Lin C-M, Lin M-H, Yeh R-G (2012) Synchronization of unified chaotic system via adaptive wavelet cerebellar model articulation controller. Neural Comput Appl. doi:10.1007/s00521-012-1021-3

  21. Lughofer E, Angelov P (2011) Handling drifts and shifts in online data streams with evolving fuzzy systems. Appl Soft Comput 11(2):2057–2068

    Article  Google Scholar 

  22. Lughofer E (2012) Single pass active learning with conflict and ignorance. Evol Syst 3:251–271

    Article  Google Scholar 

  23. Lughofer E (2012) A dynamic split-and-merge approach for evolving cluster models. Evol Syst 3:135–151

    Article  Google Scholar 

  24. Maciel L, Lemos A, Gomide F, Ballini R (2012) Evolving fuzzy systems for pricing fixed income options. Evol Syst 3:5–18

    Article  Google Scholar 

  25. Macnab CJB (2011) Neural-adaptive control using alternate weights. Neural Comput Appl 20:211–221

    Article  MathSciNet  Google Scholar 

  26. Pérez-Cruz JH, Poznyak A (2010) Control of nuclear research reactors based on a generalized hopfield neural network. Intell Autom Soft Comput 16(1):39–60

    Article  Google Scholar 

  27. Pérez Cruz JH, Ruiz Velázquez E, Rubio JJ, de Alba Padilla CA (2012) Robust adaptive neurocontrol of SISO nonlinear systems preceded by unknown deadzone. Math Probl Eng 2012:1–23

    Article  Google Scholar 

  28. Pérez-Cruz JH, Rubio JJ, Ruiz-VelPázquez E, Solís-Perales G. (2012) Tracking control based on recurrent neural networks for nonlinear systems with multiple inputs and unknown deadzone. Abstr Appl Anal 2012:1–18

    Article  Google Scholar 

  29. Pérez-Cruz JH, Alanis AY, Rubio JJ, Pacheco J (2012) System identification using multilayer differential neural networks: a new result. J Appl Math 2012:1–20

    Article  Google Scholar 

  30. Pérez-Olvera CA (2009) Control visual difuso de un sistema no-lineal, CIC-IPN, Master thesis

  31. Pérez-Olvera CA, Moreno-Armendáriz MA, Rubio-Espino E, Zaragoza-Díaz JO (2008) Modulo de visión por computadora en tiempo real para el control de un sistema plano-esfera. Res Comput Sci 38:283–293

    Google Scholar 

  32. Rubio JJ, Yu W (2006) A new discrete-time sliding-mode control with time-varying gain and neural identification. Int J Control 79(4):338–348

    Article  MATH  Google Scholar 

  33. Rubio JJ, Yu W (2007) Stability analysis of nonlinear system identification via delayed neural networks. IEEE Trans Circuits Syst II 54(2):161–165

    Article  Google Scholar 

  34. Rubio JJ, Angelov P, Pacheco J (2011) An uniformly stable backpropagation algorithm to train a feedforward neural network. IEEE Trans Neural Netw 22(3):356–366

    Article  Google Scholar 

  35. Rubio JJ, Torres C, Aguilar C (2011) Optimal control based in a mathematical model applied to robotic arms. Int J Innov Comput Info Control 7(8):5045–5062

    Google Scholar 

  36. Rubio JJ (2012) Modified optimal control with a backpropagation network for robotic arms. IET Control Theory Appl 6(14):2216–2225

    Article  MathSciNet  Google Scholar 

  37. Rubio JJ, Figueroa M, Pérez-Cruz JH, Bejarano FJ (2012) Geometric approach and structure at infinite controls for the disturbance rejection. IET Control Theory Appl 6(16):2528–2537

    Article  MathSciNet  Google Scholar 

  38. Rubio JJ, Figueroa M, Pérez Cruz JH, Rumbo J (2012) Control to stabilize and mitigate disturbances in a rotatory inverted pendulum. Mexican J Phys E 58(2):107–112

    Google Scholar 

  39. Wang LX (1994) Adaptive fuzzy systems and control. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  40. Wang C, Lin Y (2012) Decentralised adaptive dynamic surface control for a class of interconnected non-linear systems. IET Control Theory Appl 6(9):1172–1181

    Google Scholar 

  41. Yoo SJ (2012) Adaptive neural output-feedback control for a class of non-linear systems with unknown time-varying delays. IET Control Theory Appl 6(1):130–140

    Article  MathSciNet  Google Scholar 

  42. Yen M-C, Hsu C-F, Chung I-H (2012) Design of a CMAC-based smooth adaptive neural controller with a saturation compensator. Neural Comput Appl 21:35–44

    Article  Google Scholar 

  43. Yu W, Panuncio F, Li X (2011) Two-stage neural sliding-mode control of magnetic levitation in minimal invasive surgery. Neural Comput Appl 20:1141–1147

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to the editors and reviewers for their valuable comments and insightful suggestions, which helped to improve this research significantly. The authors thank the Secretaría de Investigación y Posgrado, Comisión de Operación y Fomento de Actividades Académicas del IPN, and Consejo Nacional de Ciencia y Tecnología for their help in this research. The first author thanks the Secretaría de Investigación y Posgrado of the IPN under Research Grand No. 20113187.

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Authors and Affiliations

  1. Sección de Estudios de Posgrado e Investigación, ESIME Azcapotzalco, Instituto Politecnico Nacional, Av. de las Granjas no.682, Col. Santa Catarina, 02250, Mexico, DF, Mexico

    José de Jesús Rubio

  2. Escuela Superior de Ingeniería Mecánica y Eléctrica, Zacatenco, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n, 07738, Mexico, DF, Mexico

    Floriberto Ortiz Rodríguez, Carlos R. Mariaca Gaspar & Julio César Tovar

  3. Laboratorio de Tiempo Real y Automatización, Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n Col. Zacatenco, 07738, Mexico, DF, Mexico

    Marco A. Moreno Armendáriz

Authors
  1. Floriberto Ortiz Rodríguez
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  2. José de Jesús Rubio
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  3. Carlos R. Mariaca Gaspar
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  4. Julio César Tovar
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  5. Marco A. Moreno Armendáriz
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Correspondence to José de Jesús Rubio.

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Rodríguez, F.O., de Jesús Rubio, J., Gaspar, C.R.M. et al. Hierarchical fuzzy CMAC control for nonlinear systems. Neural Comput & Applic 23 (Suppl 1), 323–331 (2013). https://doi.org/10.1007/s00521-013-1423-x

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  • DOI: https://doi.org/10.1007/s00521-013-1423-x

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