Advertisement

Observation and Identification via HOSM Observers

  • Yuri Shtessel
  • Christopher Edwards
  • Leonid Fridman
  • Arie Levant
Part of the Control Engineering book series (CONTRENGIN)

Abstract

Control systems normally perform under uncertainties/disturbances and with measurement signals corrupted by noise. For systems with reliable models and noisy measurements, a filtration approach (Kalman filters, for example) is efficient. However, as shown in Chap. 3, sliding mode observers based on first-order sliding modes are effective in the presence of uncertainties/disturbances. Nevertheless, as discussed in that chapter, they are only applicable when the relative degree of the outputs with respect to the uncertainties/disturbances is one, and differentiation of noisy outputs signals is not needed.

Keywords

Unknown Input Slide Mode Observer Luenberger Observer Uncertain Part Deterministic Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 24.
    Bejarano, J., Fridman, L.: High order sliding mode observer for linear systems with unbounded unknown inputs. Int. J. Control 83(9), 1920–1929 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 25.
    Bejarano, J., Fridman, L., Poznyak, A.: Exact state estimation for linear systems with unknown inputs based on hierarchical super-twisting algorithm. Int. J. Robust. Nonlin. 17(18), 1734–1753 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 41.
    Cannas, B., Cincotti, S., Usai, E.: An algebraic observability approach to chaos synchronisation by sliding differentiators. IEEE Trans. Circ. Systems-I: Fundamental Theory and Applications 49(7), 1000–1006 (2002)CrossRefGoogle Scholar
  4. 42.
    Cannas, B., Cincotti, S., Usai, E.: A chaotic modulation scheme based on algebraic observability and sliding mode differentiators. Chaos Soliton. Fract. 26(2), 363–377 (2005)zbMATHCrossRefGoogle Scholar
  5. 48.
    Chen, B.M.: Robust and control. Series: Communication and Control Engineering. Springer, Berlin (2000)CrossRefGoogle Scholar
  6. 52.
    Davila, J., Fridman, L., Levant, A.: Second-order sliding-modes observer for mechanical systems. IEEE Trans. Automat. Contr. 50(11), 1785–1789 (2005)MathSciNetCrossRefGoogle Scholar
  7. 53.
    Davila, J., Fridman, L., Pisano A., Usai, E.: Finite-time state observation for nonlinear uncertain systems via higher order sliding modes. Int. J. Control 82(8), 1564–1574 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 54.
    Davila, J., Rios, H., Fridman, L.: State observation for nonlinear switched systems using non-homogeneous higher order sliding mode observers. Asian J. Control 14(4), 911–923 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 79.
    Ferreira, A., Bejarano, F.J., Fridman, L.: Robust control with exact uncertainties compensation: with or without chattering? IEEE Trans. Contr. Syst. Tech. 19(5), 969–975 (2011)CrossRefGoogle Scholar
  10. 80.
    Ferreira, A., Bejarano, F.J., Fridman, L.: Unmatched uncertainties compensation based on high-order sliding mode observation. Int. J. Robust. Nonlin. (2012). doi: 10.1002/rnc.2795Google Scholar
  11. 83.
    Floquet, T., Barbot, J.P.: Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs. Int. J. Syst. Sci. 38(10): 803–815 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 84.
    Floquet, T., Edwards, C., Spurgeon, S.K.: On sliding mode observers for systems with unknown inputs. Int J. Adapt. Control Signal Process. 21, 638–656 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 94.
    Fridman, L., Levant, A., Davila, J.: Observation of linear systems with unknown inputs via high-order sliding-modes, Int. J. Syst. Sci. 38(10), 773–791 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 95.
    Fridman, L., Shtessel, Y., Edwards, C., Yan, X.G.: Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int. J. Robust. Nonlin. 18(4/5), 399–413 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 96.
    Fridman, L., Davila, J., Levant, A.: High-order sliding-mode observation for linear systems with unknown inputs. Nonlinear Anal. Hybrid Syst. 5(2), 174–188 (2011)MathSciNetCrossRefGoogle Scholar
  16. 107.
    Hautus, M.: Strong detectability and observers. Linear Algebra. Appl. 50(4), 353–368 (1983)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 111.
    Imine, H., Fridman, L., Shraim, H., Djemai, M.: Sliding mode based analysis and identification of vehicle dynamics. Lecture Notes in Control and Information Sciences, vol. 414. Springer, Berlin (2011)Google Scholar
  18. 112.
    Isidori, A.: Nonlinear Control Systems. Springer, New York (1995)zbMATHCrossRefGoogle Scholar
  19. 166.
    Shtessel, Y., Baev, S., Edwards, C., Spurgeon, S.: HOSM observer for a class of non-minimum phase causal nonlinear systems. IEEE Trans. Automat. Contr. 55(2),543–548(2010)Google Scholar
  20. 173.
    Soderstrom, T., Stoica, P.: System Identification. Prentice Hall International, Cambridge (1989)Google Scholar
  21. 180.
    Tomei, P. Marino, R.: Nonlinear Control Design: Geometric, Adaptive and Robust. Prentice Hall, London (1995)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yuri Shtessel
    • 1
  • Christopher Edwards
    • 2
  • Leonid Fridman
    • 3
  • Arie Levant
    • 4
  1. 1.Department of Electrical and Computer EngineeringUniversity of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.College of Engineering, Mathematics and Physical ScienceUniversity of ExeterExeterUK
  3. 3.Department of Control Division of Electrical EngineeringFaculty of Engineering National Autonomous University of MexicoFederal DistrictMexico
  4. 4.Department of Applied Mathematics School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations