Skip to main content
SpringerLink
Log in

Regulation and tracking of nonlinear systems

  • Living reference work entry
  • First Online:
Encyclopedia of Systems and Control

  • 394 Accesses

Abstract

A classical problem in control theory is the design of feedback laws such that the effect of exogenous inputs on selected output variables is asymptotically rejected. This includes problems of asymptotic tracking and disturbance rejection. In this entry, the fundamentals of the theory are presented, as well as constructive procedures for the design of a controller, which embeds an “internal model” of the generator of the exogenous inputs. Current and future research directions are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Bibliography

  • Byrnes CI, Isidori A (2003) Limit sets, zero dynamics and internal models in the problem of nonlinear output regulation. IEEE Trans Autom Control 48:1712–1723

    Article  MathSciNet  Google Scholar 

  • Byrnes CI, Isidori A (2004) Nonlinear internal models for output regulation. IEEE Trans Autom Control 49:2244–2247

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Chen Z, Huang J (2004) Global robust servomechanism problem of lower triangular systems in the general case. Syst Control Lett 52:209–220

    Article  MATH  Google Scholar 

  • Delli Priscoli F (2004) Output regulation with nonlinear internal models. Syst Control Lett 53: 177–185

    Article  MATH  MathSciNet  Google Scholar 

  • Delli Priscoli F, Marconi L, Isidori A (2006a) A new approach to adaptive nonlinear regulation. SIAM J Control Optim 45:829–855

    Article  MATH  MathSciNet  Google Scholar 

  • Delli Priscoli F, Marconi L, Isidori A (2006b) Nonlinear observers as nonlinear internal models. Syst Control Lett 55:640–649

    Article  MATH  MathSciNet  Google Scholar 

  • Francis BA, Wonham WM (1976) The internal model principle of control theory. Automatica 12:457–465

    Article  MATH  MathSciNet  Google Scholar 

  • Hale JK, Magalhães LT, Oliva WM (2002) Dynamics in infinite dimensions. Springer, New York

    MATH  Google Scholar 

  • Huang J (2004) Nonlinear output regulation: theory and applications. SIAM, Philadelphia

    Book  Google Scholar 

  • Huang J, Lin CF (1994) On a robust nonlinear multivariable servomechanism problem. IEEE Trans Autom Control 39:1510–1513

    Article  MATH  MathSciNet  Google Scholar 

  • Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin/New York

    Book  MATH  Google Scholar 

  • Isidori A (2013) Nonlinear zero dynamics. In: Encyclopedia of systems and control. Springer

    Google Scholar 

  • Isidori A, Byrnes CI (1990) Output regulation of nonlinear systems. IEEE Trans Autom Control 25:131–140

    Article  MathSciNet  Google Scholar 

  • Isidori A, Byrnes CI (2008) Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection. Ann Rev Control 32:1–16

    Article  Google Scholar 

  • Isidori A, Marconi L (2008) System regulation and design, geometric and algebraic methods’. In: Encyclopedia of complexity and system science. Section control and dynamical systems. Springer, Heidelberg

    Google Scholar 

  • Isidori A, Marconi L (2012) Shifting the internal model from control input to controlled output in nonlinear output regulation. In: Proceedings of the 51th IEEE conference on decision and control, Maui

    Google Scholar 

  • Isidori A, Marconi L, Serrani A (2003) Robust autonomous guidance: an internal model-based approach. Limited series advances in industrial control. Springer, London

    Book  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Marconi L, Praly L (2008) Uniform practical output regulation. IEEE Trans Autom Control 53(5):1184–1202

    Article  MathSciNet  Google Scholar 

  • Marconi L, Praly L, Isidori A (2007) Output stabilization via nonlinear luenberger observers. SIAM J Control Optim 45(6):2277–2298

    Article  MATH  MathSciNet  Google Scholar 

  • Pavlov A, van de Wouw N, Nijmeijer H (2006) Uniform output regulation of nonlinear systems: a convergent dynamics approach. Birkhauser, Boston

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Serrani A, Isidori A, Marconi L (2001) Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans Autom Control 46:1178–1194

    Article  MATH  MathSciNet  Google Scholar 

  • Teel AR, Praly L (1995) Tools for semiglobal stabilization by partial state and output feedback. SIAM J Control Optim 33:1443–1485

    Article  MATH  MathSciNet  Google Scholar 

  • Wieland P (2010) From static to dynamic couplings in consensus and synchronization among identical and non-identical systems. PhD thesis, Universität Stuttgart

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. C.A.SY. - DEI, University of Bologna, Bologna, Italy

    Lorenzo Marconi

Authors
  1. Lorenzo Marconi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lorenzo Marconi .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag London

About this entry

Cite this entry

Marconi, L. (2013). Regulation and tracking of nonlinear systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_86-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_86-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation