Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Robust Adaptive Control

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_118-1

Abstract

Robust adaptive control pertains to satisfactory behavior of adaptive control systems in the presence of nonparametric perturbations such as disturbances, unmodeled dynamics, and time delays. This article covers the highlights of robust adaptive controllers, methods used, and results obtained. Both methods of achieving robustness, which includes modifications in the adaptive law and persistent excitation in the reference input, are presented. In both cases, results obtained for robustness to disturbances and unmodeled dynamics are discussed.

Keywords

Robustness Global boundedness s-modification Dead zone Parameter projection Persistent excitation 
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Bibliography

  1. Anderson BDO, Bitmead RR, Johnson CR Jr, Kokotovic PV, Kosut RL, Mareels IM, Praly L, Riedle BD (1986) Stability of adaptive systems: passivity and averaging analysis. MIT, CambridgeGoogle Scholar
  2. Arnold VI (1982) Geometric methods in the theory of differential equations. Springer, New YorkGoogle Scholar
  3. Egardt B (1979) Stability of adaptive controllers. Springer, New YorkCrossRefMATHGoogle Scholar
  4. Hale JK (1969) Ordinary differential equations. Wiley–Interscience, New YorkMATHGoogle Scholar
  5. Hussain H, Matsutani M, Annaswamy A, Lavretsky E (2013) Adaptive control of scalar plants in the presence of unmodeled dynamics. In: 11th IFAC international workshop, ALCOSP, Caen, France, Jul 2013Google Scholar
  6. Ioannou P, Sun J (2013) Robust adaptive control. Dover, MineolaGoogle Scholar
  7. Khalil H (2001) Nonlinear systems, ch. 14.5. Prentice Hall, Upper Saddle RiverGoogle Scholar
  8. Kokotovic P, Riedle B, Praly L (1985) On a stability criterion for continuous slow adaptation. Syst Control Lett 6:7–14CrossRefMATHMathSciNetGoogle Scholar
  9. Kreisselmeier G, Narendra KS (1982) Stable model reference adaptive control in the presence of bounded disturbances. IEEE Trans Autom Control 27:1169–1175CrossRefMATHMathSciNetGoogle Scholar
  10. Krylov AN, Bogoliuboff NN (1943) Introduction to nonlinear mechanics. Princeton University Press, PrincetonGoogle Scholar
  11. Lavretsky E (2010) Adaptive output feedback design using asymptotic properties of LQG/LTR controllers. IEEE Trans Autom Control 57:1587–1591CrossRefMathSciNetGoogle Scholar
  12. Matsutani M (2013) Robust adaptive flight control systems in the presence of time delay. Ph.D. dissertation, Massachusetts Institute of TechnologyGoogle Scholar
  13. Matsutani M, Annaswamy A, Gibson T, Lavretsky E (2011) Adaptive systems with guaranteed delay margins. In: 50th IEEE conference on decision and control and European control conference, Orlando, FLGoogle Scholar
  14. Matsutani M, Annaswamy A, Lavretsky E (2012) Guaranteed delay margins for adaptive control of scalar plants. In: 2012 IEEE 51st annual conference on decision and control (CDC), Maui, Hawaii, pp 7297–7302Google Scholar
  15. Matsutani M, Annaswamy A, Lavretsky E (2013) Guaranteed delay margins for adaptive systems with state variables accessible. In: American control conference, Washington, DCGoogle Scholar
  16. Narendra KS, Annaswamy AM (2005) A new adaptive law for robust adaptation without persistent excitation. IEEE Trans Autom Control, 32:134–145CrossRefMathSciNetGoogle Scholar
  17. Narendra KS, Annaswamy AM (2005) Stable adaptive systems. Dover, MineolaMATHGoogle Scholar
  18. Narendra KS, Kudva P (1972) Stable adaptive schemes for system identification and control – parts I & II. IEEE Trans Syst Man Cybern 4:542–560CrossRefMathSciNetGoogle Scholar
  19. Peterson B, Narendra K (1982) Bounded error adaptive control. IEEE Trans Autom Control 27(6):1161–1169CrossRefMATHGoogle Scholar
  20. Pomet J, Praly L (1992) Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans Autom Control 37(6):729–740CrossRefMATHMathSciNetGoogle Scholar
  21. Rohrs C, Valavani L, Athans M, Stein G (1985) Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics. IEEE Trans Autom Control 30(9):881–889CrossRefMATHGoogle Scholar
  22. Tsakalis K, Ioannou P (1987) Adaptive control of linear time-varying plants. Automatica 23(4):459–468CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Active-adaptive Control Laboratory Department of Mechanical Engineering, Massachusetts Institute of TechnologyCambridge, MAUSA