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Essential and Redundant Internal Models in Nonlinear Output Regulation

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Analysis and Design of Nonlinear Control Systems

Abstract

Summary. This paper is focused on the problem of output regulation for nonlinear systems within the main framework developed in [23]. The main goal is to complement that theory with some new results showing how the dimension of the internal model-based regulator can be reduced by preserving the so-called internal model property. It is shown how the problem of reducing the regulator dimension can be approached by identifying “observability” parts of the so-called steady-state input generator system. A local analysis based on canonical geometric tools and local observability decomposition is also presented to identify lower bounds on the regulator dimension. Possible benefits in designing redundant internal models are also discussed.

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References

  • V. Andrieu and L. Praly. On the existence of a Kazantis-Kravaris/Luenberger observer. SIAM J. Contr. Optimization, 45:432–456, 2006.

    MathSciNet  Google Scholar 

  • W.M. Boothby. An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, 1975.

    Google Scholar 

  • C.I. Byrnes, F. Delli Priscoli, A. Isidori, and W. Kang. Structurally stable output regulation of nonlinear systems. Automatica, 33:369–385, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  • C.I. Byrnes and A. Isidori. Limit sets, zero dynamics and internal models in the problem of nonlinear output regulation. IEEE Trans. on Automat. Contr., 48:1712–1723, 2003.

    Article  MathSciNet  Google Scholar 

  • C.I. Byrnes and A. Isidori. Nonlinear internal models for output regulation. IEEE Trans. on Automat. Contr., 49:2244–2247, 2004.

    Article  MathSciNet  Google Scholar 

  • Z. Chen and J. Huang. Global robust servomechanism problem of lower triangular systems in the general case. Systems & Control Letters, 52:209–220, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Delli Priscoli. Output regulation with nonlinear internal models. Systems & Control Letters, 53:177–185, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Delli Priscoli, L. Marconi, and A. Isidori. New approach to adaptive nonlinear regulation. SIAM J. Contr. Optimization, 45:829–855, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Delli Priscoli, L. Marconi, and A. Isidori. Nonlinear observers as nonlinear internal models. Systems & Control Letters, 55:640–649, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  • B. Doubrovine, S. Novikov, and A. Fomenko. Modern Geometry-Methods and Applications. Part I: The Geometry of Surfaces, Transformation Groups and Fields, volume 93 of Graduate Texts in Mathematics. Springer Verlag, 2nd edition, 1992.

    Google Scholar 

  • M. Fliess and I. Kupka. A finiteness criterion for nonlinear input-output differential systems. SIAM J. Contr. Optimization, 21:721–728, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  • B.A. Francis and W.M. Wonham. The internal model principle of control theory. Automatica, 12:457–465, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  • J.K. Hale, L.T. Magalhães, and W.M. Oliva. Dynamics in Infinite Dimensions. Springer Verlag, New York, 2002.

    MATH  Google Scholar 

  • R. Hermann and A.J. Krener. Nonlinear controllability and observability. IEEE Trans. on Automat. Contr., 22:728–740, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Huang and C.F. Lin. On a robust nonlinear multivariable servomechanism problem. IEEE Trans. on Automat. Contr., 39:1510–1513, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Isidori. Nonlinear Control Sytems. Springer Verlag, New York, 3rd edition, 1995.

    Google Scholar 

  • A. Isidori. Nonlinear Control Systems II. Springer Verlag, New York, 1st edition, 1999.

    MATH  Google Scholar 

  • A. Isidori and C.I. Byrnes. Output regulation of nonlinear systems. IEEE Trans. on Automat. Contr., 25:131–140, 1990.

    Article  MathSciNet  Google Scholar 

  • A. Isidori, L. Marconi, and A. Serrani. Robust Autonomous Guidance: An Internal Model-based Approach. Limited series Advances in Industrial Control. Springer Verlag, London, 2003.

    Google Scholar 

  • K. Kazantzis and C. Kravaris. Nonlinear observer design using Lyapunov’s auxiliary theorem. Systems & Control Letters, 34:241–247, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • H. Khalil. Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica, 30:587–1599, 1994.

    Article  MathSciNet  Google Scholar 

  • L. Marconi and L. Praly. Uniform practical nonlinear output regulation. IEEE Trans. on Automat. Contr., 2006. Submitted.

    Google Scholar 

  • L. Marconi, L. Praly, and A. Isidori. Output stabilization via nonlinear Luenberger observers. SIAM J. Contr. Optimization, 45:2277–2298, 2007.

    Article  MathSciNet  Google Scholar 

  • A. Serrani, A. Isidori, and L. Marconi. Semiglobal output regulation for minimum-phase systems. Int. J. of Robust and Nonlinear Control, 10:379–396, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Serrani, A. Isidori, and L. Marconi. Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans. on Automat. Contr., 46:1178–1194, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Spivak. (A Comprehensive Introduction to) Differential Geometry, volume 1. Publish or Perish, Inc., 2nd edition, 1979.

    Google Scholar 

  • A.R. Teel and L. Praly. Tools for semiglobal stabilization by partial state and output feedback. SIAM J. Contr. Optimization, 33:1443–1485, 1995.

    Article  MATH  MathSciNet  Google Scholar 

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Marconi, L., Praly, L. (2008). Essential and Redundant Internal Models in Nonlinear Output Regulation. In: Astolfi, A., Marconi, L. (eds) Analysis and Design of Nonlinear Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74358-3_16

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  • DOI: https://doi.org/10.1007/978-3-540-74358-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74357-6

  • Online ISBN: 978-3-540-74358-3

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