Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Low-Power High-Gain Observers

  • Daniele Astolfi
  • Lorenzo MarconiEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100070-1

Abstract

This entry deals with a class of nonlinear high-gain observers referred to as “low-power” due to the fact that the high-gain parameter is powered only up to 2 regardless of the dimension of the observed system, on the contrary of conventional high-gain observers in which the high-gain parameter is powered up to the dimension of the observed system. This kind of observers preserves the main properties of conventional high-gain observers in terms of tunability of the speed of convergence and robustness to exogenous disturbances, by outperforming those in terms of numerical implementation and sensitivity to high-frequency measurement noise. The drawback of low-power high-gain observers over the conventional ones is given by the dimension of its dynamics that is larger.

Keywords

Nonlinear Observers High-Gain Observers Noise Sensitivity 
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Bibliography

  1. Astolfi D, Marconi L (2015) A high-gain nonlinear observer with limited gain power. IEEE Trans Autom Control 60(11):3059–3064MathSciNetCrossRefGoogle Scholar
  2. Astolfi D, Marconi L, Teel AR (2016a) Low-power peaking-free high-gain observers for nonlinear systems. In: 2016 European control conference (ECC), 1424–1429Google Scholar
  3. Astolfi D, Marconi L, Praly L, Teel A (2016b) Sensitivity to high-frequency measurement noise of nonlinear high-gain observers. IFAC-PapersOnLine 49(18): 862–866CrossRefGoogle Scholar
  4. Astolfi D, Isidori A, Marconi L (2017) Output regulation via low-power construction. In: Feedback stabilization of controlled dynamical systems. Springer, Cham, pp 143–165CrossRefGoogle Scholar
  5. Astolfi D, Marconi L, Praly L, Teel AR (2018) Low-power peaking-free high-gain observers. Automatica 98: 169–179MathSciNetCrossRefGoogle Scholar
  6. Atassi AN, Khalil HK (1999) A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans Autom Control 44(9):1672–1687MathSciNetCrossRefGoogle Scholar
  7. Edwards C, Spurgeon S, Patton RJ (2000) Sliding mode observers for fault detection and isolation. Automatica 36(4):541–553MathSciNetCrossRefGoogle Scholar
  8. Gauthier JP, Kupka I (2001) Deterministic observation theory and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Isidori A (2017) Regulation and tracking in nonlinear systems. In: Lectures in feedback design for multivariable systems. Springer, Cham, pp 341–364CrossRefGoogle Scholar
  10. Khalil HK, Praly L (2014) High-gain observers in nonlinear feedback control. Int J Robust Nonlinear Control 24(6):993–1015MathSciNetCrossRefGoogle Scholar
  11. Teel AR, Praly L (1995) Tools for semiglobal stabilization by partial state and output feedback. SIAM J Control Optim 33(5):1443–1488MathSciNetCrossRefGoogle Scholar
  12. Wang L, Astolfi D, Su H, Marconi L (2017) High-gain observers with limited gain power for systems with observability canonical form. Automatica 75:16–23MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.CNRS, LAGEPP UMR 5007VilleurbanneFrance
  2. 2.CASY-DEIUniversity of BolognaBolognaItaly

Section editors and affiliations

  • Alberto Isidori
    • 1
  1. 1.Department of Computer, Control, Management Engng. “A. Ruberti”University of Rome “La Sapienza”RomeItaly