Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Nonlinear Adaptive Control

  • A. Astolfi
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_117


We consider the control of nonlinear systems in which parameters are uncertain and may vary. For such systems the control must adapt to the parameter change to deliver closed-loop performance, such as asymptotic stability or tracking. A concise description of available methods and basic adaptive stabilization results, which can be used as building blocks for complex adaptive control problems, are discussed.


Adaptive stabilization Linear parameterization Lyapunov function Nonlinear parameterization Output feedback 
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  1. Astolfi A, Karagiannis D, Ortega R (2008) Nonlinear and adaptive control with applications. Springer, LondonGoogle Scholar
  2. Hovakimyan N, Cao C (2010) L1 adaptive control theory. SIAM, PhiladelphiaGoogle Scholar
  3. Ilchmann A (1997) Universal adaptive stabilization of nonlinear systems. Dyn Control 7(3): 199–213MathSciNetGoogle Scholar
  4. Ilchmann A, Ryan EP (1994) Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise. Automatica 30(2):337–346MathSciNetGoogle Scholar
  5. Jiang Z-P, Praly L (1998) Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34(7):825–840MathSciNetGoogle Scholar
  6. Kanellakopoulos I, Kokotović PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253Google Scholar
  7. Krstić M, Kanellakopoulos I, Kokotović P (1995) Nonlinear and adaptive control design. Wiley, New YorkGoogle Scholar
  8. Marino R, Tomei P (1995) Nonlinear control design: geometric, adaptive and robust. Prentice-Hall, LondonGoogle Scholar
  9. Nussbaum RD Some remarks on a conjecture in parameter adaptive control. Syst Control Lett 3(5):243–246 (1982)Google Scholar
  10. Pomet J-B, Praly L (1992) Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans Autom Control 37(6):729–740MathSciNetGoogle Scholar
  11. Sastry SS, Isidori A (1989) Adaptive control of linearizable systems. IEEE Trans Autom Control 34(11):1123–1131MathSciNetGoogle Scholar
  12. Spooner JT, Maggiore M, Ordonez R, Passino KM (2002) Stable adaptive control and estimation for nonlinear systems. Wiley, New YorkGoogle Scholar
  13. Townley S (1999) An example of a globally stabilizing adaptive controller with a generically destabilizing parameter estimate. IEEE Trans Autom Control 44(11):2238–2241MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • A. Astolfi
    • 1
    • 2
  1. 1.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK
  2. 2.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità di Roma Tor VergataRomaItaly