Skip to main content
SpringerLink
Log in

Adaptive Control based on Extended Neural Network for SISO Uncertain Nonlinear Systems

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper proposes a novel adaptive control criterion for a class of single-input-single-output (SISO) uncertain nonlinear systems by using extended neural networks (ENNs). Distinguished from the traditional neural networks, our ENNs are composed of radial basis function neural networks (RBFNNs), scalers and saturators. And these ENNs are used to approximate the uncertainties in the nonlinear systems. Based on the Lyapunov stability theory and our ENNs, an adaptive control scheme is designed to guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). It is also worth pointing out that our control method makes the construction of RBFNNs and the design of adaptive laws separated, which means only the outputs of ENNs and one update law of the parameter in the scaler are to be adjusted. Thus, our control scheme can effectively reduce the online computation burden of the adaptive parameters. Finally, simulation examples are given to verify the effectiveness of our theoretical result.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Saat, S. K. Nguang, C. Lin, and Z. Zakaria, “Robust nonlinear H ∞ state feedback control of polynomial discretetime systems: an integrator approach,” Circuits, Systems, and Signal Processing, vol. 33, no. 2, pp. 331–346, February 2014. [click]

    Article  MathSciNet  Google Scholar 

  2. S. Saat and S. K. Nguang, “Nonlinear output feedback control with integrator for polynomial discrete-time systems,” International Journal of Robust and Nonlinear Control, vol. 25, no. 7, pp. 1051–1065, May 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Fernando, K. Godpromesse, and L. Francoise, “A novel online training neural network-based algorithm for wind speed estimation and adaptive control of PMSG wind turbine system for maximum,” Renewable. Energy, vol. 86, pp. 38–48, February 2016. [click]

    Article  Google Scholar 

  4. B. Chen, H. Zhang, and C. Lin, “Observer-based adaptive neural network control for nonlinear systems in nonstrictfeedback form,” IEEE Trans. on Neural Networks and Learning Systems, vol. 27, no. 1, pp. 89–98, January 2016. [click]

    Article  MathSciNet  Google Scholar 

  5. A. Sahoo, H. Xu, and S. Jagannathan, “Adaptive neural network-based event-triggered control of single-input single-output nonlinear discrete-time systems,” IEEE Trans. on Neural Networks and Learning Systems, vol. 27, no. 1, pp. 151–164, January 2016. [click]

    Article  MathSciNet  Google Scholar 

  6. A. Sun, L. Lu, and C. Li, “Synchronization of an uncertain small-world neuronal network based on modified sliding mode control technique,” Nonlinear Dynamics, vol. 82, no. 4, pp. 1905–1912, December 2015.

    Article  MathSciNet  MATH  Google Scholar 

  7. W. Assawinchaichote, S. K. Nguang, and P. Shi, “Fuzzy control and filter design for uncertain fuzzy systems,” Springer, Lecture Notes in Control and Information Sciences, ISBN: 978-3-540-37011-6 (Print) 978-3-540-37012-3 (Online), 2006.

    Google Scholar 

  8. S. K. Nguang, W. Assawinchaichote, P. Shi, and Y. Shi, “Robust H ∞ control design for uncertain fuzzy systems with Markovian jumps: an LMI approach,” American Control Conference, pp. 1805–1810, 2005. [click]

    Google Scholar 

  9. W. Zeng and Q. Wang, “Learning from adaptive neural network control of an underactuated rigid spacecraft,” Neurocomputing, vol. 168, no. 30, pp. 690–697, November 2015. [click]

    Article  Google Scholar 

  10. Y. Fang, J. Fei, and K. Ma, “Model reference adaptive sliding mode control using RBF neural network for active power filter,” International Journal of Electrical Power & Energy Systems, vol. 73, pp. 249–258, December 2015. [click]

    Article  Google Scholar 

  11. Y. Zhang and S. Wang, “MLP technique baseed reinforcement learning control of discrete pure-feedback systems,” Neurocomputing, vol. 168, pp. 401–407, November 2015. [click]

    Article  Google Scholar 

  12. J. Fei and H. Ding, “Adaptive sliding mode control of dynamic system using RBF neural network,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1563–1573, October 2012. [click]

    Article  MathSciNet  Google Scholar 

  13. H. Wang, B. Chen, and C. Lin, “Direct adaptive neural control for strict-feedback stochastic nonlinear systems,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2703–2718, March 2012.

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Yu, S. Fei, J. Huang, and Y. Gao, “Trajectory switching control of robotic manipulators based on RBF neural networks,” Circuits, Systems, and Signal Processing, vol. 33, no. 4, pp. 1119–1133, April 2014. [click]

    Article  MathSciNet  Google Scholar 

  15. M. Wang, X. Liu, and P. Shi, “Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 6, pp. 1681–1692, December 2011. [click]

    Article  Google Scholar 

  16. H. Jafarnejadsani, J. Pieper, and J. Ehlers, “Adaptive control of a variable-speed variable-pitch wind turbine using radial-basis function neural network,” IEEE Trans. on Control Systems Technology, vol. 21, no. 6, pp. 2264–2272, November 2013. [click]

    Article  Google Scholar 

  17. Q. Zhu, S. Fei, T. Zhang, and T. Li, “Adaptive RBF neuralnetworks control for a class of time-delay nonlinear systems,” Neurocomputing, vol. 71, no. 16-18, pp. 3617–3624, October 2008.

    Article  Google Scholar 

  18. M. Pai, “Dynamic output feedback RBF neural network sliding mode control for robust tracking and model following,” Nonlinear Dynamics, vol. 79, no. 2, pp. 1023–1033, January 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. Y. Pan, T. Sun, and H. Yu, “Peaking-free output-feedback adaptive neural control under a nonseparation principle,” IEEE Trans. on Neural Networks and Learning Systems, vol. 26, no. 12, pp. 3097–3108, December 2015. [click]

    Article  MathSciNet  Google Scholar 

  20. N. T. Tai and K. K. Ahn, “A RBF neural network sliding mode controller for SMA actuator,” International Journal of Control, Automation and Systems, vol. 8, no. 6, pp. 1296–1305, December 2010.

    Article  Google Scholar 

  21. J. Platt, “A resource-allocating network for function interpolation,” Neural Computation, vol. 3, no. 2, pp. 213–225, June 1991. [click]

    Article  MathSciNet  Google Scholar 

  22. Y. Lu, N. Sundararajan, and P. Saratchandran, “A sequential learning scheme for function approximation using minimal radial basis function neural networks,” Neural Computation, vol. 9, no. 2, pp. 461–478, February 1997. [click]

    Article  MATH  Google Scholar 

  23. H. Feng, “Self-generation RBFNs using evolutional PSO learning,” Neurocomputing, vol. 70, no. 1-3, pp. 241–251, December 2006. [click]

    Article  Google Scholar 

  24. S. Chen, X. Hong, B. L. Luk, and C. J. Harris, “Construction of tunable radial basis function networks using orthogonal forward selection,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 39, no. 2, pp. 457–466, April 2009. [click]

    Article  Google Scholar 

  25. D. Du, K. Li, and M. Fei, “A fast multi-output RBF neural network construction method,” Neurocomputing, vol. 73, no. 10-12, pp. 2196–2202, June 2010. [click]

    Article  Google Scholar 

  26. D. Shi, D. S. Yeung, and J. Gao, “Sensitivity analysis applied to the construction of radial basis function networks,” Neural Networks, vol. 18, no. 7, pp. 951–957, September 2005. [click]

    Article  MATH  Google Scholar 

  27. Y. Wang, L. Luo, Y. Fan, Y. Zhang, X. Liu, and S. Zhang, “Adaptive control design for a class of nonlinear systems based on fuzzy logic systems with scalers and saturators,” International Journal of Systems Science, vol. 45, no. 3, pp. 202–214, March 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. S. X. Ng, M. Yee, and L. Hanzo, “Coded modulation assisted radial basis function aided turbo equalization for dispersive Rayleigh-fading channels,” IEEE Trans. on Wireless Communications, vol. 3, no. 6, pp. 2198–2206, November 2004. [click]

    Article  Google Scholar 

  29. J. Gonzalez, I. Rojas, J. Ortega, H. Pomares, F. J. Fernandez, and A. F. Diaz, “Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation,” IEEE Trans. on Neural Networks, vol. 14, no. 6, pp. 1478–1495, November 2003. [click]

    Article  Google Scholar 

  30. X. Hong, S. Chen, and C. J. Harris, “A fast linear-in-theparameters classifier construction algorithm using orthogonal forward selection to minimize leave-one-out misclassification rate,” International Journal of Systems Science, vol. 39, no. 2, pp. 119–125, February 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  31. J. E. Slotine, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ., 1991.

    MATH  Google Scholar 

  32. Y. Wei, J. Qiu, P. Shi, and H. Lam, “A new design of Hinfinity piecewise filtering for discrete-time nonlinear timevarying delay systems via T-S fuzzy affine models,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2034–2047, August 2017. [click]

    Article  Google Scholar 

  33. Y. Wei, J. Qiu, H. Lam, and L. Wu, “Approaches to T-S fuzzy-affine-model-based reliable output feedback control for nonlinear itô stochastic systems,” IEEE Trans. on Fuzzy Systems, vol. 25, no. 3, pp. 569–583, June 2017. [click]

    Article  Google Scholar 

  34. Y. Wei, J. Qiu, and H. R. Karimi, “Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults,” IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 64, no. 1, pp. 170–181, January 2017. [click]

    Article  Google Scholar 

  35. M. Chemachema, “Output feedback direct adaptive neural network control for uncertain SISO nonlinear systems using a fuzzy estimator of the control error,” Neural Networks, vol. 36, pp. 25–34, December 2012. [click]

    Article  MATH  Google Scholar 

  36. C. Wang, H. Liu, and T. Lin, “Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems,” IEEE Trans. on Fuzzy Systems, vol. 10, no. 1, pp. 39–49, February 2002. [click]

    Article  Google Scholar 

  37. M. Wang, C. Wang, and X. Liu, “Dynamic learning from adaptive neural control with predefined performance for a class of nonlinear systems,” Information Sciences, vol. 279, pp. 874–888, September 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  38. Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information,” Information Sciences, vol. 269, pp. 316–331, June 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  39. Y. Wei, J. Qiu, H. R. Karimi, and M. Wang, “New results on H ∞ dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information,” Optimal Control Applications And Methods, vol. 35, pp. 656–675, November 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Guangdong University of Technology, Guangzhou Higher Education Mega Center, Panyu District, Guangzhou, 510006, China

    Hao-guang Chen, Yin-he Wang & Li-li Zhang

Authors
  1. Hao-guang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yin-he Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li-li Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hao-guang Chen.

Additional information

Recommended by Associate Editor Sing Kiong Nguang Editor Hamid Reza Karimi. This work was supported by the National Natural Science Foundation of China (61273219, 61673120, 61603098), the Natural Science Foundation of Guangdong Province of China (2016A030310336) and Specialized Research Fund for the Doctoral Program of Higher Education of China (20134420110003).

Hao-guang Chen is currently working toward a Ph.D. degree in the School of Automation, Guangdong University of Technology, Guangzhou, P. R. China. His research interests include nonlinear dynamical systems, neural network, fuzzy logic systems and adaptive control.

Yin-he Wang received his M. S. degree in mathematics from Sichuan Normal University, Chengdu, P. R. China, in 1990, and the Ph.D. degree in control theory and engineering from Northeastern University, Shenyang, P. R. China, in 1999. From 2000 to 2002, he was a Post-doctor in Department of Automatic control, Northwestern Polytechnic University, Xi’an, P. R. China. From 2005 to 2006, he was a visiting scholar at Department of Electrical Engineering, Lakehead University, Canada. He is currently a Professor with the Faculty of Automation, Guangdong University of Technology, Guangzhou, China. His research interests include fuzzy adaptive robust control, analysis for nonlinear systems and complex dynamical networks.

Li-li Zhang received the M.S. degree in applied mathematics from University of Science and Technology Beijing, Beijing, P. R. China, in 2004, and the Ph.D. degree in school of automation, Guangdong University of Technology, Guangzhou, China, in 2014. She is currently an associate professor in School of Applied Mathematics, Guangdong University of Technology, Guangzhou, China. Her research interests include control and synchronization for complex dynamical networks and chaotic systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Hg., Wang, Yh. & Zhang, Ll. Adaptive Control based on Extended Neural Network for SISO Uncertain Nonlinear Systems. Int. J. Control Autom. Syst. 16, 27–38 (2018). https://doi.org/10.1007/s12555-016-0721-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0721-3

Keywords

Search

Navigation