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Disturbance attenuation for discrete-time feedforward nonlinear systems

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Stability and Stabilization of Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 246))

Abstract

In this paper the inverse optimal stabilization problem is solved for nonlinear nonaffine control discrete-time systems which are globally stable when uncontrolled. Stabilizing feedback laws and nonquadratic cost functionals are constructed. The result is applied to feedforward systems.

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References

  1. B.D.O. Anderson and J.B. Moore: Linear Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1971.

    MATH  Google Scholar 

  2. R.A. Freeman and P.V. Kokotovic: Inverse optimality in robust stabilization, SIAM Journal on Control and Optimization, vol. 34, pp. 1365–1391, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. R.A. Freeman and P.V. Kokotovic: Robust Nonlinear Control Design, Birkhauser, Boston, 1996.

    MATH  Google Scholar 

  4. W.M. Haddad, V. Chellaboina and J.L. Fausz: Optimal Nonlinear Disturbance Rejection Control for Nonlinear Cascade Systems, Int. J. Contr., 68 (1997) 997–1018.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Jankovic, R. Sepulchre and P.V. Kokotovic: Global stabilization of an enlarged class of cascade nonlinear systems. IEEE Trans. on Automatic Control, vol.41, no.12, pp.1723–1735, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. V. Jurdjevic, J.P. Quinn: Controllability and stability. J. Differential Equations, vol.4, pp. 381–389, 1978.

    Article  MathSciNet  Google Scholar 

  7. R.E. Kalman: When is a linear control systtem optimal? Trans. ASME Ser. D: J. Basic En., vol. 86, pp. 1–10, 1964.

    Google Scholar 

  8. M. Krstić and Zhong-Hua Li: Inverse optimal design of input-to-state stabilizing nonlinear controllers, Preprint 1997.

    Google Scholar 

  9. Zhong-Hua Li and M. Krstić: Optimal design of adaptive tracking controllers for nonlinear systems, Proc. ACC, Albuquerque, New Mexico, 1997.

    Google Scholar 

  10. Wei Lin: Further results on global stabilization of discrete-time nonlinear systems. Systems & Control Letters, 29, 51–59, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  11. Wei Lin and C. Byrnes: Passivity and Absolute Stabilization of a Class of Discrete-time Nonlinear Systems. Automatica, Vol. 31.No.2, pp. 263–267, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  12. F. Mazenc: Stabilization of Feedforward Systems Approximated by a Nonlinear Chain of Integrators. Systems & Control Letters 32 (1997) 223–229.

    Article  MATH  MathSciNet  Google Scholar 

  13. F. Mazenc and L. Praly: Adding an integration and Global asymptotic stabilization of feedforward systems. IEEE Trans. on Automatic Control, vol.41,no.11, pp.1559–1578, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Mazenc and H. Nijmeijer: Forwarding in discrete-time nonlinear systems. Int. J. Control, 1998, vol. 71,No.5, pp. 823–835.

    Article  MATH  MathSciNet  Google Scholar 

  15. F. Mazenc, R. Sepulchre and M. Jankovic: Lyapunov functions for stable cascades and applications to global stabilization. 36th CDC conference, San Diego, 1997 and to appear in IEEE Trans. Automatic Control.

    Google Scholar 

  16. P.J. Moylan and B.D. Anderson: Nonlinear regulator theory and an inverse optimal control problem. IEEE Trans. Automatic Control, vol. 18, pp. 460–465, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. Sepulchre, M. Jankovic and P.V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, 1997.

    Google Scholar 

  18. H.J. Susmann, E.D. Sontag and Y. Yang: A general result on the stabilization of linear systems using bounded control. IEEE Trans. on Automatic Control, vol. 39, pp. 2411–2425, 1994.

    Article  Google Scholar 

  19. A. Teel: Feedback Stabilization: Nonlinear Solutions to Inherently Nonlinear Problems. PhD Dissertation, University of California, Berkeley, 1992.

    Google Scholar 

  20. A. Teel: On L 2 performance induced by feedbacks with multiple saturations. ESAIM: Control, Optimisation and Clculus of Variations, vol. 1, pp. 225–240, Spetembre 1996.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, C.N.R.S., SUPELEC, 91192, Gif-sur-Yvette, France

    Tarek Ahmed-Ali

  2. Centre for Process Systems Engineering, Imperial College of Science Technology and Medecine, London, SW7 2AZ, UK

    Frédéric Mazenc

Authors
  1. Tarek Ahmed-Ali
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  2. Frédéric Mazenc
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  3. Françoise Lamnabhi-Lagarrigue
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Editor information

Editors and Affiliations

  1. Dept. of Systems Dynamics, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052, Gent, Belgium

    Dirk Aeyels (Professor) (Professor)

  2. Laboratoire des Signaux et Systèmes, CNRS, SUPELEC, 91192, Gif-sur-Yvette, France

    Françoise Lamnabhi-Lagarrigue (Docteur d’état) (Docteur d’état)

  3. Dept. of Applied Mathematics, University of Twente, PO Box 217, 7500, Enschede, The Netherlands

    Arjan van der Schaft (Professor) (Professor)

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© 1999 Springer-Verlag London Limited

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Ahmed-Ali, T., Mazenc, F., Lamnabhi-Lagarrigue, F. (1999). Disturbance attenuation for discrete-time feedforward nonlinear systems. In: Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (eds) Stability and Stabilization of Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 246. Springer, London. https://doi.org/10.1007/1-84628-577-1_1

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  • DOI: https://doi.org/10.1007/1-84628-577-1_1

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-638-7

  • Online ISBN: 978-1-84628-577-6

  • eBook Packages: Springer Book Archive

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