Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 951983, 10 pages
http://dx.doi.org/10.1155/2014/951983
Research Article

Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

1Sección de Estudios de Posgrado e Investigación, ESIME UA-IPN, Avenida de las Granjas, No. 682, Colonia Santa Catarina, México, DF 02250, Mexico
2Departamento de Control Automático, CINVESTAV-IPN, Avenida Instituto Politécnico Nacional, No. 2508, México, DF 07360, Mexico

Received 27 February 2014; Accepted 21 May 2014; Published 19 June 2014

Academic Editor: Chin-Chia Wu

Copyright © 2014 J. Humberto Pérez-Cruz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990. View at Publisher · View at Google Scholar · View at Scopus
  2. M. M. Polycarpou and P. A. Ioannou, “Identification and control of nonlinear systems using neural network models: design and stability analysis,” Tech. Rep. 91-09-01, Department of Electrical Engineering, University of Southern California, Los Angeles, Calif, USA, 1991. View at Google Scholar
  3. G. A. Rovithakis and M. A. Christodoulou, “Adaptive control of unknown plants using dynamical neural networks,” IEEE Transactions on Systems, Man and Cybernetics, vol. 24, no. 3, pp. 400–412, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, “High-order neural network structures for identification of dynamical systems,” IEEE Transactions on Neural Networks, vol. 6, no. 2, pp. 422–431, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Yu and A. Poznyak, “Indirect adaptive control via parallel dynamic neural networks,” IEE Proceedings: Control Theory and Applications, vol. 146, no. 1, pp. 25–30, 1999. View at Google Scholar
  6. X. Li and W. Yu, “Dynamic system identification via recurrent multilayer perceptrons,” Information Sciences, vol. 147, no. 1–4, pp. 45–63, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. G. A. Rovithakis, “Robust redesign of a neural network controller in the presence of unmodeled dynamics,” IEEE Transactions on Neural Networks, vol. 15, no. 6, pp. 1482–1490, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. E. N. Sanchez and M. A. Bernal, “Adaptive recurrent neural control for nonlinear system tracking,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 30, no. 6, pp. 886–889, 2000. View at Publisher · View at Google Scholar · View at Scopus
  9. B. S. Leon, A. Y. Alanis, E. N. Sanchez, E. Ruiz-Velazquez, and F. Ornelas-Tellez, “Inverse optimal neural control for a class of discrete-time nonlinear positive systems,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 7, pp. 614–629, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Y. Alanis, M. Lopez-Franco, N. Arana-Daniel, and C. Lopez-Franco, “Discrete-time neural control for electrically driven nonholonomic mobile robots,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 7, pp. 630–644, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. W. Yu and J. Rosen, “Neural PID control of robot manipulators with application to an upper limb exoskeleton,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 43, no. 2, pp. 673–684, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. G. A. Rovithakis, E. Stelios, and M. A. Christodoulou, “Application of a neural-network scheduler on a real manufacturing system,” IEEE Transactions on Control Systems Technology, vol. 9, no. 2, pp. 261–270, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. I. Chairez, R. Fuentes, T. Poznyak, M. Franco, and A. Poznyak, “Numerical modeling of the benzene reaction with ozone in gas phase using differential neural networks,” Catalysis Today, vol. 151, no. 1-2, pp. 159–165, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Fei and Z. Wang, “Adaptive neural sliding mode control of active power filter,” Journal of Applied Mathematics, vol. 2013, Article ID 341831, 8 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. M. M. Polycarpou, “Stable adaptive neural control scheme for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 447–451, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Dinh, S. Bhasin, and W. E. Dixon, “Dynamic neural network-based robust identification and control of a class of nonlinear systems,” in Proceedings of the 49th IEEE Conference on Decision and Control (CDC '10), pp. 5536–5541, Atlanta, Ga, USA, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. J. T. Spooner and K. M. Passino, “Stable adaptive control using fuzzy systems and neural networks,” IEEE Transactions on Fuzzy Systems, vol. 4, no. 3, pp. 339–359, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Yeşildirek and F. L. Lewis, “Feedback linearization using neural networks,” Automatica, vol. 31, no. 11, pp. 1659–1664, 1995. View at Google Scholar · View at Scopus
  19. E. B. Kosmatopoulos, “Universal stabilization using control Lyapunov functions, adaptive derivative feedback and neural network approximators,” in Proceedings of the 35th IEEE Conference on Decision and Control (CDC '96), vol. 3, pp. 2444–2449, Kobe, Japan, December 1996. View at Publisher · View at Google Scholar · View at Scopus
  20. R. A. Felix, E. N. Sanchez, and A. G. Loukianov, “Avoiding controller singularities in adaptive recurrent neural control,” in Proceedings of the 16th International Federation of Automatic Control World Congress (IFAC '05), pp. 109–114, July 2005. View at Scopus
  21. R. C. Rodríguez and W. Yu, “Robust adaptive control via neural linearization and compensation,” Journal of Control Science and Engineering, vol. 2012, Article ID 867178, 9 pages, 2012. View at Publisher · View at Google Scholar
  22. T. Zhang, S. S. Ge, and C. C. Hang, “Adaptive neural network control for strict-feedback nonlinear systems using backstepping design,” Automatica, vol. 36, no. 12, pp. 1835–1846, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. Y.-J. Liu and W. Wang, “Adaptive neural network control for nonlinear systems based on approximation errors,” in Advances in Neural Networks—ISNN 2006, vol. 3972 of Lecture Notes in Computer Science, pp. 836–841, Springer, Berlin, Germany, 2006. View at Publisher · View at Google Scholar
  24. J. Humberto Pérez-Cruz and A. Poznyak, “Control of nuclear research reactors based on a generalized Hopfield neural network,” Intelligent Automation and Soft Computing, vol. 16, no. 1, pp. 39–60, 2010. View at Google Scholar · View at Scopus
  25. J. H. Perez-Cruz, I. Chairez, A. Poznyak, and J. J. de Rubio, “Constrained neural control for the adaptive tracking of power profiles in a triga reactor,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 7, pp. 4575–4788, 2011. View at Google Scholar · View at Scopus
  26. H. Zhou, J.-Y. Hou, Y.-G. Zhao, and Y.-L. Chen, “Model-based trajectory tracking control for an electrohydraulic lifting system with valve compensation strategy,” Journal of Central South University, vol. 19, no. 11, pp. 3110–3117, 2012. View at Google Scholar
  27. A. C. Valdiero, C. S. Ritter, C. F. Rios, and M. Rafikov, “Nonlinear mathematical modeling in pneumatic servo position applications,” Mathematical Problems in Engineering, vol. 2011, Article ID 472903, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Liu, Y.-J. Liu, and C. L. P. Chen, “Adaptive neural network control for a DC motor system with dead-zone,” Nonlinear Dynamics, vol. 72, no. 1-2, pp. 141–147, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. G. Xia, X. Shao, A. Zhao, and H. Wu, “Adaptive neural network control with backstepping for surface ships with input dead-zone,” Mathematical Problems in Engineering, vol. 2013, Article ID 530162, 9 pages, 2013. View at Publisher · View at Google Scholar
  30. G. Tao and P. V. Kokotovic, “Adaptive control of plants with unknown dead-zones,” IEEE Transactions on Automatic Control, vol. 39, no. 1, pp. 59–68, 1994. View at Publisher · View at Google Scholar · View at Scopus
  31. G. Tao and P. V. Kokotovic, Adaptive Control of Systems with Actuator and Sensor Nonlinearities, John Wiley & Sons, New York, NY, USA, 1996.
  32. Y.-J. Sun, “Composite tracking control for generalized practical synchronization of duffing-holmes systems with parameter mismatching, unknown external excitation, plant uncertainties, and uncertain deadzone nonlinearities,” Abstract and Applied Analysis, vol. 2012, Article ID 640568, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. H. Cho and E. R.-W. Bai, “Convergence results for an adaptive dead zone inverse,” International Journal of Adaptive Control and Signal Processing, vol. 12, no. 5, pp. 451–466, 1998. View at Google Scholar · View at Scopus
  34. X.-S. Wang, H. Hong, and C.-Y. Su, “Model reference adaptive control of continuous-time systems with an unknown input dead-zone,” IEE Proceedings: Control Theory and Applications, vol. 150, no. 3, pp. 261–266, 2003. View at Publisher · View at Google Scholar · View at Scopus
  35. J. Zhou and X. Z. Shen, “Robust adaptive control of nonlinear uncertain plants with unknown dead-zone,” IET Control Theory & Applications, vol. 1, no. 1, pp. 25–32, 2007. View at Publisher · View at Google Scholar · View at Scopus
  36. X.-S. Wang, C.-Y. Su, and H. Hong, “Robust adaptive control of a class of nonlinear systems with unknown dead-zone,” Automatica, vol. 40, no. 3, pp. 407–413, 2004. View at Publisher · View at Google Scholar · View at Scopus
  37. Z. Wang, Y. Zhang, and H. Fang, “Neural adaptive control for a class of nonlinear systems with unknown dead zone,” Neural Computing and Applications, vol. 17, no. 4, pp. 339–345, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. Y.-J. Liu and N. Zhou, “Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input,” ISA Transactions, vol. 49, no. 4, pp. 462–469, 2010. View at Publisher · View at Google Scholar · View at Scopus
  39. J. H. Pérez-Cruz, E. Ruiz-Velázquez, J. de Jesús Rubio, and C. A. de Alba-Padilla, “Robust adaptive neurocontrol of SISO nonlinear systems preceded by unknown deadzone,” Mathematical Problems in Engineering, vol. 2012, Article ID 342739, 23 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  40. R. R. Šelmić and F. L. Lewis, “Deadzone compensation in motion control systems using neural networks,” IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 602–613, 2000. View at Publisher · View at Google Scholar · View at Scopus
  41. T. P. Zhang and S. S. Ge, “Robust adaptive neural control of SISO nonlinear systems with unknown nonlinear dead-zone and gain sign,” in Proceedings of the IEEE Symposium on Intelligent Control, pp. 315–320, Munich, Germany, October 2006.
  42. F. L. Lewis, J. Campos, and R. Selmic, Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities, SIAM, 2002.
  43. J. H. Pérez-Cruz, J. de Jesús Rubio, E. Ruiz-Velázquez, and G. Solís-Perales, “Tracking control based on recurrent neural networks for nonlinear systems with multiple inputs and unknown deadzone,” Abstract and Applied Analysis, vol. 2012, Article ID 471281, 18 pages, 2012. View at Publisher · View at Google Scholar
  44. I. Chairez, A. Poznyak, and T. Poznyak, “New sliding-mode learning law for dynamic neural network observer,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 12, pp. 1338–1342, 2006. View at Publisher · View at Google Scholar · View at Scopus
  45. I. Chairez, A. Poznyak, and T. Poznyak, “Stable weights dynamics for a class of differential neural network observer,” IET Control Theory & Applications, vol. 3, no. 10, pp. 1437–1447, 2009. View at Publisher · View at Google Scholar · View at Scopus
  46. G. A. Rovithakis, “Tracking control of multi-input affine nonlinear dynamical systems with unknown nonlinearities using dynamical neural networks,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 29, no. 2, pp. 179–189, 1999. View at Publisher · View at Google Scholar · View at Scopus