Advertisement

A Unifying Approach to the Design of Nonlinear Output Regulators

  • Lorenzo Marconi
  • Alberto Isidori
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 353)

Abstract

The goal of this paper is to propose a unique vision able to frame a number of results recently proposed in literature to tackle problems of output regulation for nonlinear systems. This is achieved by introducing the so-called asymptotic internal model property as the crucial property which, if fulfilled, leads to the design of the regulator for a fairly general class of nonlinear systems satisfying a proper minimum-phase condition. It is shown that recent frameworks based upon the use of nonlinear high-gain and adaptive observer techniques for the regulator design can be cast in this setting. A recently proposed technique for output regulation without immersion is also framed in these terms.

Keywords

Internal Model SIAM Journal Output Regulation Output Feedback Controller Adaptive Observer 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrieu V, Praly L (2006) On the existence of a Kazantis-Kravaris/Luenberger observer, SIAM Journal on Control and Optimization, 45: 432–456MathSciNetGoogle Scholar
  2. 2.
    Bastin G, Gevers M R (1988) Stable adaptive observers for nonlinear time varying systems, IEEE Transactions on Automatic Control, 33: 650–657zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bonivento C, Isidori A, Marconi L, Paoli A (2004) Implicit fault tolerant control: application to induction motors, Automatica, 40: 355–371.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Byrnes C I, Isidori A (2003) Limit sets, zero dynamics and internal models in the problem of nonlinear output regulation, IEEE Transactions on Automatic Control, 48: 1712–1723CrossRefMathSciNetGoogle Scholar
  5. 5.
    Byrnes C I, Isidori A (2004) Nonlinear internal models for output regulation, IEEE Transactions on Automatic Control, 49: 2244–2247CrossRefMathSciNetGoogle Scholar
  6. 6.
    Byrnes C I, Delli Priscoli F, Isidori A, Kang W (1997) Structurally stable output regulation of nonlinear systems, Automatica, 33: 369–385zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chen Z, Huang J (2004) Global robust servomechanism problem of lower triangular systems in the general case, Systems and Control Letters, 52: 209–220zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Delli Priscoli F, Marconi L, Isidori A (2006) A new approach to adaptive nonlinear regulation, SIAM Journal on Control and Optimization, 45: 829–855zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Delli Priscoli F, Marconi L, Isidori A (2006) Nonlinear observers as nonlinear internal models, Systems and Control Letters, 55: 640–649zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Delli Priscoli F (2004) Output regulation with nonlinear internal models, Systems and Control Letters, 53: 177–185zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fliess M, Kupka I (1983) A finitness criterion for nonlinear input-output differential systems, SIAM Journal on Control and Optimization, 21: 721–728zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Francis B A (1977) The linear multivariable regulator problem, SIAM Journal on Control and Optimization, 14: 486–505CrossRefMathSciNetGoogle Scholar
  13. 13.
    Francis BA, Wonham WM (1976) The internal model principle of control theory, Automatica, 12: 457–465zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gauthier J P, Kupka I (2001), Deterministic Observation Theory and Applications. Cambridge University PressGoogle Scholar
  15. 15.
    Hale J K, Magalhães L T, Oliva W M (2002) Dynamics in Infinite Dimensions. Springer Verlag, New YorkzbMATHGoogle Scholar
  16. 16.
    Huang J, Lin C F (1994) On a robust nonlinear multivariable servomechanism problem, IEEE Transactions on Automatic Control, 39: 1510–1513zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Isidori A, Marconi L, Serrani A (2003) Robust Autonomous Guidance: An Internal Model-based Approach. Springer Verlag London, Limited series Advances in Industrial ControlGoogle Scholar
  18. 18.
    Isidori A, Byrnes C I (1990) Output Regulation of Nonlinear Systems, IEEE Transactions on Automatic Control, 25: 131–140CrossRefMathSciNetGoogle Scholar
  19. 19.
    Kazantzis K, Kravaris C (1998) Nonlinear Observer Design Using Lyapunov’s Auxiliary Theorem, Systems and Control Letters, 34: 241–247zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Khalil H (1994) Robust Servomechanism Output Feedback Controllers for Feedback Linearizable Systems, Automatica, 30: 587–1599CrossRefMathSciNetGoogle Scholar
  21. 21.
    Marconi L, Praly L, Isidori A (2006) Output Stabilization via Nonlinear Luenberger Observers, SIAM Journal on Control and Optimization, To appearGoogle Scholar
  22. 22.
    Marino R, Tomei P (1992) Global Adaptive Observers for Nonlinear Systems via Filtered Transformations, IEEE Transactions on Automatic Control, 37: 1239–1245CrossRefMathSciNetGoogle Scholar
  23. 23.
    Serrani A, Isidori A, Marconi L (2000) Semiglobal Output Regulation for Minimum-Phase Systems, International Journal on Robust and Nonlinear Control, 10, pp. 379–396zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Serrani A, Isidori A, Marconi L (2001) Semiglobal Nonlinear Output Regulation with Adaptive Internal Model, IEEE Transactions on Automatic Control, 46: 1178–1194zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Teel A R, Praly L (1995) Tools for Semiglobal Stabilization by Partial State and Output Feedback, SIAM Journal on Control and Optimization, 33: 1443–1485zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Lorenzo Marconi
    • 1
  • Alberto Isidori
    • 1
    • 2
    • 3
  1. 1.CASY-DEISUniversità of BolognaItaly
  2. 2.DISSapienza - Università di RomaItaly
  3. 3.ESEWashington UniversitySt. LouisUSA

Personalised recommendations