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Variable Structure Systems: Towards the 21st Century pp 201–222Cite as

Robust Control of Infinite-Dimensional Systems via Sliding Modes

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 274))

Abstract

Infinite-dimensional control systems, driven by a discontinuous feedback, are under study. Discontinuous control algotithms are developed. The algorithms ensure desired dynamic properties as well as robustness of the closed-loop system against matched disturbances. The theory presented is illustrated by applications to heat processes and mechanical distributed oscillators.

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References

  1. Breger, A.M., Butkovskii, A.G., Kubyshkin, V.A., and Utkin, V.I. (1980), Sliding modes for control of distributed parameter entities subjected to a mobile multicycle signal. Automation and Remote Contr. 41, 346–355

    Google Scholar 

  2. Curtain, R. F. and Pritchard, A. J. (1978) Infinite-dimensional linear systems theory. Lecture notes in control and information sciences, Springer-Verlag, Berlin

    MATH  Google Scholar 

  3. Dorling, C.M. and Zinober, A.S.I. (1986) Two Approaches to Sliding Mode Design in Multivariable Variable Structure Control Systems. International Journal of Control 44, 65–82

    Article  MATH  Google Scholar 

  4. Drazenovic, B. (1969) The Invariance Conditions for Variable Structure Systems. Automatica, 5, 287–295

    Article  MATH  MathSciNet  Google Scholar 

  5. Foias, C., Özbay, H., and Tannenbaum, A. (1996) Robust Control of Infinite Dimensional Systems: Frequency Domain Methods. Springer-Verlag, London

    MATH  Google Scholar 

  6. Friedman, A. (1969) Partial Differential Equations. Holt, Reinhart, and Winston, New York

    MATH  Google Scholar 

  7. Gutman, S. (1979) Uncertain dynamic systems-a Lyapunov min-max approach. IEEE Trans. Autom. Contr. AC-24, 437–449

    Article  MathSciNet  Google Scholar 

  8. Gutman, S. and Leitmann, G. (1976) Stabilizing Feedback Control for Dynamic Systems with Bounded Uncertainties. Proceedings of IEEE Conference on Decision and Control, 94–99

    Google Scholar 

  9. Henry D. (1981) Geometric theory of semilinear parabolic equations. Lecture notes in math. Springer-Verlag, Berlin

    MATH  Google Scholar 

  10. van Keulen, B. (1993) H∞-Control for Distributed Parameter Systems: A State-Space Approach. Birkhauser, Boston

    Google Scholar 

  11. Kirillov, A.A. and Gvishiani, A.D. (1982) Theorems and Problems in Functional Analysis. Springer-Verlag, New York

    MATH  Google Scholar 

  12. Orlov, Yu.V. (1983) Application of Lyapunov method in distributed systems. Automation and Remote Control44,426–430

    MATH  Google Scholar 

  13. Orlov, Yu.V. (1993) Sliding mode-model reference adaptive control of distributed parameter systems. Proc. 32nd IEEE Conf. on Decision and Control, 2438–2445

    Google Scholar 

  14. Orlov, Yu.V. (2000) Sliding mode observer-based synthesis of state-derivative free model reference adaptive control of distributed parameter systems. Journal of Dynamic Systems, Measurement, and Control, 122, 725–731

    Article  Google Scholar 

  15. Orlov, Yu.V. (2000) Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Trans. Autom. Contr. AC-45, 834–843

    Article  MathSciNet  Google Scholar 

  16. Orlov, Yu.V. and Utkin, V.I. (1982) Use of sliding modes in distributed system control problems. Automation and Remote Contr. 43, 1127–1135

    MATH  MathSciNet  Google Scholar 

  17. Orlov, Yu.V. and Utkin, V.I. (1987) Sliding mode control in infinite-dimensional systems. Automatica 23, 753–757

    Article  MATH  MathSciNet  Google Scholar 

  18. Orlov, Yu.V. and Utkin, V.I. (1998) Unit sliding mode control in infinite-dimensional systems. Applied Mathematics and Computer Science. 8, 7–20

    MATH  MathSciNet  Google Scholar 

  19. Ryan, E.P. and Corless, M. (1984) Ultimate Boundness and Asymptotic Stability of a Class of Uncertain Systems via Continuous and Discontinuous Feedback Contr. IMA J. Math. Cont. and Inf. 1, 222–242

    Google Scholar 

  20. Utkin, V.I. (1992) Sliding Modes in Control Optimization. Springer-Verlag, Berlin

    MATH  Google Scholar 

  21. Utkin V. I. and Orlov Yu. V. (1990) Sliding mode control of infinite-dimensional systems. Nauka, Moscow (in Russian)

    Google Scholar 

  22. Zinober, A.S.I., ed. (1990) Deterministic Control of Uncertain Systems. Peter Peregrinus Press, London

    MATH  Google Scholar 

  23. Zolezzi, T. (1989) Variable structure control of semilinear evolution equations. Partial differential equations and the calculus of variations, Essays in honor of Ennio De Giorgi, Birkhauser, Boston 2, 997–1018

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. CICESE Mexican Research Center, P.O.Box 434944, San Diego, CA, 92143, USA

    Yuri Orlov

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  1. Yuri Orlov
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Editor information

Editors and Affiliations

  1. Faculty for Informatics and Communication, Central Queensland University, Rockhampton, Australia

    Xinghuo Yu (Associate Professor) (Associate Professor)

  2. Department of Electrical Engineering, National University of Singapore, Singapore

    Jian-Xin Xu (Associate Professor) (Associate Professor)

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© 2002 Springer-Verlag Berlin Heidelberg

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Orlov, Y. (2002). Robust Control of Infinite-Dimensional Systems via Sliding Modes. In: Yu, X., Xu, JX. (eds) Variable Structure Systems: Towards the 21st Century. Lecture Notes in Control and Information Sciences, vol 274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45666-X_9

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  • DOI: https://doi.org/10.1007/3-540-45666-X_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42965-4

  • Online ISBN: 978-3-540-45666-7

  • eBook Packages: Springer Book Archive

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