Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Regulation and tracking of nonlinear systems

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_86-1


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.


Nonlinear output regulation Tracking Robust control Stabilization of nonlinear systems 
This is a preview of subscription content, log in to check access.


  1. Byrnes CI, Isidori A (2003) Limit sets, zero dynamics and internal models in the problem of nonlinear output regulation. IEEE Trans Autom Control 48:1712–1723CrossRefMathSciNetGoogle Scholar
  2. Byrnes CI, Isidori A (2004) Nonlinear internal models for output regulation. IEEE Trans Autom Control 49:2244–2247CrossRefMathSciNetGoogle Scholar
  3. Byrnes CI, Delli Priscoli F, Isidori A, Kang W (1997) Structurally stable output regulation of nonlinear systems. Automatica 33:369–385CrossRefMATHMathSciNetGoogle Scholar
  4. Chen Z, Huang J (2004) Global robust servomechanism problem of lower triangular systems in the general case. Syst Control Lett 52:209–220CrossRefMATHGoogle Scholar
  5. Delli Priscoli F (2004) Output regulation with nonlinear internal models. Syst Control Lett 53: 177–185CrossRefMATHMathSciNetGoogle Scholar
  6. Delli Priscoli F, Marconi L, Isidori A (2006a) A new approach to adaptive nonlinear regulation. SIAM J Control Optim 45:829–855CrossRefMATHMathSciNetGoogle Scholar
  7. Delli Priscoli F, Marconi L, Isidori A (2006b) Nonlinear observers as nonlinear internal models. Syst Control Lett 55:640–649CrossRefMATHMathSciNetGoogle Scholar
  8. Francis BA, Wonham WM (1976) The internal model principle of control theory. Automatica 12:457–465CrossRefMATHMathSciNetGoogle Scholar
  9. Hale JK, Magalhães LT, Oliva WM (2002) Dynamics in infinite dimensions. Springer, New YorkMATHGoogle Scholar
  10. Huang J (2004) Nonlinear output regulation: theory and applications. SIAM, PhiladelphiaCrossRefGoogle Scholar
  11. Huang J, Lin CF (1994) On a robust nonlinear multivariable servomechanism problem. IEEE Trans Autom Control 39:1510–1513CrossRefMATHMathSciNetGoogle Scholar
  12. Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin/New YorkCrossRefMATHGoogle Scholar
  13. Isidori A (2013) Nonlinear zero dynamics. In: Encyclopedia of systems and control. SpringerGoogle Scholar
  14. Isidori A, Byrnes CI (1990) Output regulation of nonlinear systems. IEEE Trans Autom Control 25:131–140CrossRefMathSciNetGoogle Scholar
  15. Isidori A, Byrnes CI (2008) Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection. Ann Rev Control 32:1–16CrossRefGoogle Scholar
  16. 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, HeidelbergGoogle Scholar
  17. 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, MauiGoogle Scholar
  18. Isidori A, Marconi L, Serrani A (2003) Robust autonomous guidance: an internal model-based approach. Limited series advances in industrial control. Springer, LondonCrossRefGoogle Scholar
  19. Khalil H (1994) Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30:587–1599CrossRefMathSciNetGoogle Scholar
  20. Marconi L, Praly L (2008) Uniform practical output regulation. IEEE Trans Autom Control 53(5):1184–1202CrossRefMathSciNetGoogle Scholar
  21. Marconi L, Praly L, Isidori A (2007) Output stabilization via nonlinear luenberger observers. SIAM J Control Optim 45(6):2277–2298CrossRefMATHMathSciNetGoogle Scholar
  22. Pavlov A, van de Wouw N, Nijmeijer H (2006) Uniform output regulation of nonlinear systems: a convergent dynamics approach. Birkhauser, BostonGoogle Scholar
  23. Serrani A, Isidori A, Marconi L (2000) Semiglobal output regulation for minimum-phase systems. Int J Robust Nonlinear Control 10:379–396CrossRefMATHMathSciNetGoogle Scholar
  24. Serrani A, Isidori A, Marconi L (2001) Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans Autom Control 46:1178–1194CrossRefMATHMathSciNetGoogle Scholar
  25. Teel AR, Praly L (1995) Tools for semiglobal stabilization by partial state and output feedback. SIAM J Control Optim 33:1443–1485CrossRefMATHMathSciNetGoogle Scholar
  26. Wieland P (2010) From static to dynamic couplings in consensus and synchronization among identical and non-identical systems. PhD thesis, Universität StuttgartGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.C.A.SY. - DEIUniversity of BolognaBolognaItaly