Abstract
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.
Notes
- 1.
Classical references on adaptive control for nonlinear systems and on recent research directions are give below.
Bibliography
Classical references on adaptive control for nonlinear systems and on recent research directions are give below.
Astolfi A, Karagiannis D, Ortega R (2008) Nonlinear and adaptive control with applications. Springer, London
Hovakimyan N, Cao C (2010) L 1 adaptive control theory. SIAM, Philadelphia
Ilchmann A (1997) Universal adaptive stabilization of nonlinear systems. Dyn Control 7(3): 199–213
Ilchmann A, Ryan EP (1994) Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise. Automatica 30(2):337–346
Jiang Z-P, Praly L (1998) Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34(7):825–840
Kanellakopoulos I, Kokotović PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253
Krstić M, Kanellakopoulos I, Kokotović P (1995) Nonlinear and adaptive control design. Wiley, New York
Marino R, Tomei P (1995) Nonlinear control design: geometric, adaptive and robust. Prentice-Hall, London
Nussbaum RD Some remarks on a conjecture in parameter adaptive control. Syst Control Lett 3(5):243–246 (1982)
Pomet J-B, Praly L (1992) Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans Autom Control 37(6):729–740
Sastry SS, Isidori A (1989) Adaptive control of linearizable systems. IEEE Trans Autom Control 34(11):1123–1131
Spooner JT, Maggiore M, Ordonez R, Passino KM (2002) Stable adaptive control and estimation for nonlinear systems. Wiley, New York
Townley S (1999) An example of a globally stabilizing adaptive controller with a generically destabilizing parameter estimate. IEEE Trans Autom Control 44(11):2238–2241
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this entry
Cite this entry
Astolfi, A. (2014). Nonlinear Adaptive Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_117-1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5102-9_117-1
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
Chapter history
-
Latest
Nonlinear Adaptive Control- Published:
- 12 November 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_117-2
-
Original
Nonlinear Adaptive Control- Published:
- 18 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_117-1