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Regulation and Tracking in Nonlinear Systems

  • Alberto IsidoriEmail author
Chapter
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)

Abstract

In this chapter, the problem of asymptotic tracking/rejection of exogenous commands/disturbances for nonlinear systems is discussed. Results that extend those developed earlier in Chap.  4 for linear systems are presented. The discussion follows very closely the analysis of necessary conditions presented in Sect.  4.3 and the construction of a regulator presented in the second part of Sect.  4.6. The construction of an internal model, though, requires a different and more elaborate analysis, for which two alternatives are offered. The chapter is complemented with a discussion of a simple problem of inducing consensus in a network of nonlinear agents.

Keywords

Internal Model Laplacian Matrix Output Regulation Minimum Phase Augmented System 
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. 1.
    J. Huang, W.J. Rugh, On a nonlinear multivariable servomechanism problem. Automatica 26, 963–972 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. Isidori, C.I. Byrnes, Output regulation of nonlinear systems. IEEE Trans. Autom. Control. AC-25, 131–140 (1990)Google Scholar
  3. 3.
    H. Khalil, Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30, 587–1599 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    J. Huang, C.F. Lin, On a robust nonlinear multivariable servomechanism problem. IEEE Trans. Autom. Control AC-39, 1510–1513 (1994)Google Scholar
  5. 5.
    C.I. Byrnes, F. Delli, Priscoli, A. Isidori, W. Kang, Structurally stable output regulation of nonlinear systems. Automatica 33, 369–385 (1997)Google Scholar
  6. 6.
    C.I. Byrnes, A. Isidori, Limit sets zero dynamics and internal models in the problem of nonlinear output regulation. IEEE Trans. Autom. Control 48, 1712–1723 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Isidori, L. Marconi, A. Serrani, Robust Autonomous Guidance: And Internal-Model Approach (Springer, London, 2003)CrossRefzbMATHGoogle Scholar
  8. 8.
    J. Huang, Nonlinear Output Regulation: Theory and Applications (SIAM, Philadephia, 2004)CrossRefzbMATHGoogle Scholar
  9. 9.
    C.I. Byrnes, A. Isidori, Nonlinear internal models for output regulation. IEEE Trans. Autom. Control AC-49, 2244–2247 (2004)Google Scholar
  10. 10.
    Z. Chen, J. Huang, A general formulation and solvability of the global robust output regulation problem. IEEE Trans. Autom. Control AC-50, 448–462 (2005)Google Scholar
  11. 11.
    A. Pavlov, N. van de Wouw, H. Nijmeijer, Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach (Birkhauser, Boston, 2006)CrossRefzbMATHGoogle Scholar
  12. 12.
    L. Marconi, L. Praly, A. Isidori A, Output stabilization via nonlinear luenberger observers. SIAM J. Control Optim. 45, 2277–2298 (2006)Google Scholar
  13. 13.
    L. Marconi, L. Praly, Uniform practical nonlinear output regulation. IEEE Trans. Autom. Control 53, 1184–1202 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. Isidori, C.I. Byrnes, Steady-state behaviors in nonlinear systems, with an application to robust disturbance rejection. Annu. Rev Control 32, 1–16 (2008)CrossRefGoogle Scholar
  15. 15.
    A. Isidori, L. Marconi, G. Casadei, Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory. IEEE Trans. Autom. Control 59, 2680–2691 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Informatica, Automatica e GestionaleUniversità degli Studi di Roma “La Sapienza”RomeItaly

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