Neuro-Adaptive Output Feedback Control for a Class of Nonlinear Non-Minimum Phase Systems

  • S. M. Hoseini
  • M. Farrokhi


This paper presents an adaptive output-feedback control method for non-affine nonlinear non-minimum phase systems that have partially known Lipschitz continuous functions in their arguments. The proposed controller is comprised of a linear, a neuro-adaptive and an adaptive robustifying control term. The adaptation law for the neural network weights is obtained using the Lyapunov’s direct method. One of the main advantageous of the proposed method is that the control law does not depend on the state estimation. This task is accomplished by introducing a strictly positive-real augmented error dynamic and using the Leftshetz–Kalman–Yakobuvich lemma. The ultimate boundedness of the error signals will be shown analytically using the extension of Lyapunov theory. The effectiveness of the proposed scheme will be shown in simulations for the benchmark problem Translational Oscillator/Rotational Actuator (TORA) system.


Neural networks Nonlinear non-minimum phase system Adaptive control Output feedback Strictly positive real 


  1. 1.
    Kazantizis, N., Niemiec, M.: A new approach to zero dynamic assignment problem for nonlinear discrete-time systems using functional equations. Syst. Control Lett. 51(3–4), 311–324 (2007)Google Scholar
  2. 2.
    Talebi, H.A., Patel, R.V.: A neural network controller for a class of nonlinear non-minimum phase systems with application to a flexible-link manipulator. Int. J. Dyn. Syst. Meas. Contr. 127, 289–294 (2005)CrossRefGoogle Scholar
  3. 3.
    Patel, R.V., Misra, P.: Transmission zero assignment in linear multivariable systems Part 1: square system. In: Proc. 37th Conf. Decision and Contr., Florida (1998)Google Scholar
  4. 4.
    Norrlof, M., Markusson, O.: Iterative learning control of nonlinear non-minimum phase system and its application to system and model inversion. In: Proc. 40th Conf. Decision and Contr., Florida (2001)Google Scholar
  5. 5.
    Norrlof, M., Gunnarsson, S.: On the design of ILC algorithms using optimization. Automatica 37(12), 2011–2016 (2001)CrossRefGoogle Scholar
  6. 6.
    Sogo, T., Kinoshita K., Adachi, N.: Iterative learning control using adjoint system for nonlinear non-minimum phase systems. In: Proc. 39th Conf. Decision and Contr., Australia (2000)Google Scholar
  7. 7.
    Yang, X.-G., Spurgeon, S.K., Edwards, C.: Decentralised sliding mode control for non-minimum phase interconnected system based on reduced-order compensator. Automatica 42(10), 1821–1828 (2006)CrossRefGoogle Scholar
  8. 8.
    Lee, C.H.: Stabilization of nonlinear non-minimum phase system: adaptive parallel approach using recurrent fuzzy neural network. IEEE Trans. Syst. Man Cybern., Part B 34(2), 1075–1088 (2004)CrossRefGoogle Scholar
  9. 9.
    Chen, S.C., Chen, W.L.: Output regulation of nonlinear uncertain system with non-minimum phase via enhances RBFN controller. IEEE Trans. Syst. Man Cybern., Part A 33(2), 265–270 (2003)CrossRefGoogle Scholar
  10. 10.
    Hoseini, S.M., Farrokhi, M.: Adaptive stabilization of non-minimum phase nonlinear systems using neural networks. In: Proc. IFAC Workshop on Adaptation and Learning in Control and Signal Processing. Saint Petersburg, Russia (2007)Google Scholar
  11. 11.
    Isidori, A.: Nonlinear Control Systems. Springer, Berlin (1995)MATHGoogle Scholar
  12. 12.
    Marino, R., Tomei, P.: Nonlinear Adaptive Design: Geometric, Adaptive and Robust. Prentice-Hall, London (1995)MATHGoogle Scholar
  13. 13.
    Isidori, A.: A tool for semiglobal stabilization of uncertain non-minimum phase nonlinear systems via output feedback. IEEE Trans. Automat. Contr. 45(10), 1817–1827 (2000)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Karagiannis, D., Jiang, Z.P., Ortega, R., Astolfi, A.: Output-feedback stabilization of a class of uncertain non-minimum phase nonlinear systems. Automatica 41(9), 1609–1615 (2005)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Wang, N., Xu, W., Chen, F.: Adaptive global output feedback stabilization of some non-minimum phase nonlinear uncertain system. IET Control Theory Appl. 2(2), 117–125 (2008)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Ding, Z.: Semi global stabilization of a class of non-minimum phase nonlinear output-feedback system. IEEProc. Control Theory Appl. 152(4), 460–464 (2005)CrossRefGoogle Scholar
  17. 17.
    Yang, X.-G., Edwards, C., Spurgeon, S.K.: Output feedback stabilization of a class of uncertain non-minimum phase system with nonlinear disturbance. Int. J. Control 77(15), 1353–1361 (2004)CrossRefGoogle Scholar
  18. 18.
    Hovakimyan, N., Yang, B.J., Calise, A.J.: Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems. Automatica 42(4), 513–522 (2006)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Ge, S.S., Zhang, T.: Neural network control of non-affine nonlinear system with zero dynamics by state and output feedback. IEEE Trans. Neural Netw. 14(4), 900–918 (2003)CrossRefGoogle Scholar
  20. 20.
    Lewis, F., Yesildirek, A., Liu, K.: Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans. Neural Netw. 7(2), 388–399 (1996)CrossRefGoogle Scholar
  21. 21.
    Astrom, K.J., Wittenmark, B.: Adaptive Control. Addison-Wesley, Boston (1994)Google Scholar
  22. 22.
    Narendra, K.S., Annaswamy, A.M.: Stable Adaptive System. Prentice-Hall, London (1990)Google Scholar
  23. 23.
    Hovakimyan, N., Nardi, F., Calise, A.J.: A novel error observer based adaptive output feedback approach for control of uncertain systems. IEEE Trans. Automat. Contr. 47(8), 1310–1314 (2002)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Lavertsky, E., Calise, A.J., Hovakimyan, N.: Upper bounds for approximation of continuous-time dynamics using delayed outputs and feedforward neural networks. IEEE Trans. Automat. Contr. 48(9), 1606–1610 (2003)CrossRefGoogle Scholar
  25. 25.
    Ioannou, P.A., Kokotovic, P.V.: Adaptive Systems with Reduced Models. Springer, New York (1983)MATHCrossRefGoogle Scholar
  26. 26.
    Lewis, F., Jagannathan, S., Yesildirek, A.: Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor and Francis, London (1999)Google Scholar
  27. 27.
    Lancaster, P.: Explicit solutions of linear matrix equations. SIAM Rev. 12, 544–566 (1970)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Center of Excellence for Power System Automation and OperationIran University of Science and TechnologyTehranIran

Personalised recommendations