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Observation and Identification Via High-Order Sliding Modes

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Modern Sliding Mode Control Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 375))

Abstract

Observation of system states in the presence of unknown inputs is one of the most important problems in the modern control theory. Usually the observers for such systems are designed under assumption that only the outputs are available but not their derivatives. In particular, it is required that the unknown inputs need to match to the known outputs.

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References

  1. Utkin, V.I., Guldner, J., Shi, J.: Sliding mode control in electromechanical systems. Taylor and Francis, London (1999)

    Google Scholar 

  2. Walcott, B., Zak, S.: State observation of nonlinear uncertain dynamical systems. IEEE Trans. on Automatic Control 32, 166–170 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Edwards, C., Spurgeon, S.K.: Sliding Mode Control. Taylor and Francis, London (1998)

    Google Scholar 

  4. Barbot, J.P., Djemai, M., Boukhobza, T.: Sliding mode observers. In: Perruquetti, W., Barbot, J.P. (eds.) Sliding Mode Control in Engineering. Control Engineering Series. Marcel Dekker, New York (2002)

    Google Scholar 

  5. Shtessel, Y.B., Shkolnikov, I.A., Brown, M.D.J.: An Asymptotic Second Order Smooth Sliding Mode Control. Asian Journal of Control 5, 498–504 (2003)

    Google Scholar 

  6. Poznyak, A.S.: Stochastic output noise effects in sliding mode estimations. International Journal of Control 76, 986–999 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Edwards, C., Spurgeon, S.K., Tan, C.P.: On development and applications of sliding mode observers. In: Yu, X., Xu, J.X. (eds.) Variable Structure Systems: Towards 21st Century. Springer Lecture Notes in Control and Information Science, vol. 274. Springer, Berlin (2002)

    Chapter  Google Scholar 

  8. Edwards, C., Spurgeon, S.K., Patton, R.J.: Sliding mode observers for fault detection and isolation. Automatica 36, 541–553 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Xiong, Y., Saif, M.: Sliding mode observer for nonlinear uncertain systems. IEEE Trans. on Automatic Control 46, 2012–2017 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Tan, C.P., Edwards, C.: Sliding mode observers for robust detection and reconstruction of actuator send sensor faults. International Journal of Robust and Nonlinear Control 13, 443–463 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Alvarez, J., Orlov, Y., Acho, L.: An invariance principle for discontinuous dynamic systems with application to a coulomb friction oscillator. ASME Journal of Dynamic Systems, Measurement, and Control 122, 687–690 (2000)

    Article  Google Scholar 

  12. Xian, B., Queiroz, M., Dawson, D., McIntyre, M.: A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems. Automatica 40, 695–700 (2004)

    Article  MATH  Google Scholar 

  13. Davila, J., Fridman, L., Levant, A.: Second-order sliding mode observer for mechanical systems. IEEE Transactions on Automatic Control 50, 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

  14. Davila, J., Fridman, L., Pozniak, A.: Observation and identification of mechanical systems via second order sliding modes. International Journal of Control 79, 1251–1262 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Su, Y., Müller, P., Zheng, C.: A simple nonlinear observer for a class of uncertain mechanical systems. IEEE Trans. Aut. Contr. 52, 1340–1345 (2007)

    Article  Google Scholar 

  16. Hashimoto, H., Utkin, V.I., Xu, J.X., Suzuki, H., Harashima, F.: VSS observer for linear time varying system. In: Proc of IECON 1990, Pacific Grove, CA (1990)

    Google Scholar 

  17. Ahmed-Ali, T., Lamnabhi-Lagarrigue, F.: Sliding observer-controller design for uncertain triangular nonlinear systems. IEEE Trans. Aut. Contr. 44(6), 1244–1249 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Floquet, T., Barbot, J.P.: A canonical form for the design of unknown input sliding mode observers. In: Edwards, C., Fossas, E., Fridman, L. (eds.) Advances in variable structure and sliding mode control. Springer Lecture Notes in Control and Information Science, vol. 334. Springer, Berlin (2006)

    Chapter  Google Scholar 

  19. Bejarano, F.J., Fridman, L., Poznyak, A.: Exact State Estimation for Linear Systems with Unknown Inputs based on a hierarchical super twisting algorithm. International Journal of Robust And Nonlinear Control 17, 1734–1753 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Contr. 58, 1247–1263 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  21. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34, 379–384 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control 76, 924–941 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Fridman, L., Shtessel, Y., Edwards, C., Yan, X.G.: Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. International Journal of Robust and Nonlinear Control 18, 399–412 (2008)

    Article  Google Scholar 

  24. Fridman, L., Levant, A., Davila, J.: Observation of linear systems with unknown inputs via higher order sliding modes. International Journal of System Science 38, 773–791 (2008)

    Article  MathSciNet  Google Scholar 

  25. Fridman, L., Levant, A., Davila, J.: High-order sliding-mode observation and fault detection via weakly unobservable subspace reconstruction. In: Proc. 2007 European Control Conference ECC 2007, Kos, Greece (2007)

    Google Scholar 

  26. Molinari, B.P.: A strong controllability and observability in linear multivariable control. IEEE Trans. Aut. Contr. 21, 761–764 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  27. Bejarano, F.J., Fridman, L., Poznyak, A.: Exact State Estimation for Linear Systems with Unknown Inputs based on a hierarchical super twisting algorithm. International Journal of Robust And Nonlinear Control 17, 1734–1753 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  28. Filippov, A.F.: Differential equations with discontinuous right-hand sides. Kluwer Academic Publisher, Dordrecht (1988)

    MATH  Google Scholar 

  29. Wonham, W.M.: Linear multivariable control: A geometric approach, 1st edn. Lecture notes in economics and mathematical systems. Springer, NY (1974)

    MATH  Google Scholar 

  30. Hautus, M.: Strong detectability and observers. Linear Algebra and its Applications 50, 353–368 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  31. Trentelman, H.L., Stoorvogel, A.A., Hautus, M.: Control theory for linear systems. Springer, London (2001)

    MATH  Google Scholar 

  32. Isidori, A.: Nonlinear Control Systems II. Springer, London (1999)

    MATH  Google Scholar 

  33. Chen, C.: Linear Systems: theory and design. Oxford University Press, NY (1999)

    Google Scholar 

  34. Bejarano, F.J., Fridman, L., Poznyak, A.: Estimation of unknown inputs, with application to fault detection, via partial hierarchical observation. In: Proc European Control Conference ECC 2007, Kos, Greece (2007)

    Google Scholar 

  35. Merzouki, R., Davila, J., Fridman, L., Cadiou, J.: Backlash phenomenon observation and identication in electromechanical systems. Control Engineering Practice 15, 447–457 (2007)

    Article  Google Scholar 

  36. Benallegue, A., Mokhtari, A., Fridman, L.: High-order sliding-mode observer for a quadrotor UAV. International Journal of Robust and Nonlinear Control 18, 427–440 (2007)

    Article  Google Scholar 

  37. Rabhi, A., M’Sirdi, N., Fridman, L., Delanne, Y.: Second order sliding mode observer for estimation of road profile. In: Proc IEEE Workshop on Variable Structure Systems VSS 2006, Alghero, Italy (2006)

    Google Scholar 

  38. Bouteldja, M., Hadri, A.E., Davila, J., Cadiou, J.C., Fridman, L.: Observation and estimation of dynamics performance of heavy vehicle via second order sliding modes. In: Proc. IEEE Workshop on Variable Structure Systems VSS 2006, Alghero, Italy (2006)

    Google Scholar 

  39. Imine, H., Fridman, L.: Estimation of the unknown inputs and vertical forces of the heavy vehicle via higher order sliding mode observer. In: Proc. IEEE Intelligent Vehicles Symposium, Marmoris, Turkey (2007)

    Google Scholar 

  40. Shraim, H., Ananou, B., Fridman, L., Noura, H., Ouladsine, M.: Sliding mode observers for the estimation of vehicle parameters. In: Proc. IEEE 45th Conference on Decision in Control CDC 2006, San Diego, CA, US (2006)

    Google Scholar 

  41. Shraim, H., Ananou, B., Fridman, L., Ouladsine, M.: A new diagnosis strategy based on the online estimation of the tire pressure. In: Proc. European Control Conference ECC 2007, Kos, Greece (2007)

    Google Scholar 

  42. Chen, W., Saif, M.: Actuator fault diagnosis for uncertain linear systems using a high-order sliding-mode robust differentiator (HOSMRD). International Journal of Robust and Nonlinear Control 18, 413–426 (2007)

    Article  Google Scholar 

  43. Edwards, C., Fridman, L., Thein, M.W.L.: Fault reconstruction in a leader/follower spacecraft system using higher order sliding mode observers. In: Proc. IEEE American Control Conference ACC 2007, NewYork, USA (2007)

    Google Scholar 

  44. Lebastard, V., Aoustin, Y., Plestan, F., Fridman, L.: Absolute orientation estimation based on high order sliding mode observer for a five link walking biped robot. In: Proc. 9th. IEEE Workshop on Variable Structure Systems VSS 2006, Alghero, Italy (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Control, Division of Electrical Engineering, Engineering Faculty, National Autonomous University of Mexico, UNAM, Ciudad Universitaria, 04510, Mexico, D.F.

    Leonid Fridman & Jorge Davila

  2. Applied Mathematics Dept., School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, 69978, Israel

    Arie Levant

Authors
  1. Leonid Fridman
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  2. Arie Levant
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  3. Jorge Davila
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Editor information

Giorgio Bartolini Leonid Fridman Alessandro Pisano Elio Usai

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Fridman, L., Levant, A., Davila, J. (2008). Observation and Identification Via High-Order Sliding Modes. In: Bartolini, G., Fridman, L., Pisano, A., Usai, E. (eds) Modern Sliding Mode Control Theory. Lecture Notes in Control and Information Sciences, vol 375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79016-7_14

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  • DOI: https://doi.org/10.1007/978-3-540-79016-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79015-0

  • Online ISBN: 978-3-540-79016-7

  • eBook Packages: EngineeringEngineering (R0)

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