Skip to main content

Indirect Adaptive Control

  • Chapter
Adaptive Control

Part of the book series: Communications and Control Engineering ((CCE))

Abstract

Indirect adaptive control is a widely applicable adaptive control strategy. In real-time, it combines plant model parameter estimation in closed loop with the redesign of the controller. Adaptive pole placement and its robustified version, together with adaptive generalized predictive control constitute the core of the chapter. Adaptive linear quadratic control is also presented. Application of various strategies for the indirect adaptive control of a flexible transmission illustrates the methodology presented in this chapter.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    What is in fact needed is the knowledge of n B +d. However, the knowledge of d reduces the number of estimated parameters.

  2. 2.

    In fact \(\hat{S}(t,q^{-1})=\hat{S}^{\prime}(t,q^{-1})H_{S}(q^{-1})\), \(\hat{R}(t,q^{-1})=\hat{R}^{\prime }(t,q^{-1})H_{R}(q^{-1})\) where H S (q −1) and H R (q −1) are the fixed parts of the controller.

  3. 3.

    The index q −1 has been dropped to simplify the notation.

  4. 4.

    See Chap. 8, Sect. 8.7 for details.

  5. 5.

    These experiments have been carried out by J. Chebassier (Lab. d’Automatique de Grenoble).

References

  • Anderson BDO, Johnson CR (1982) Exponential convergence of adaptive identification and control algorithms. Automatica 18(1):1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson BDO, Johnstone RM (1985) Global adaptive pole positioning. IEEE Trans Autom Control AC-30(4):11–12

    Article  MathSciNet  Google Scholar 

  • Barmish R, Ortega R (1991) On the radius of stabilizability of LTI systems: application to projection implementation in indirect adaptive control. Int J Adapt Control Signal Process 5:251–258

    Article  MATH  Google Scholar 

  • Bitmead RR, Gevers M, Wertz V (1990) Adaptive optimal control. Prentice-Hall, New York

    MATH  Google Scholar 

  • Clarke D, Mohtadi C (1989) Properties of generalized predictive control. Automatica 25:859–876

    Article  MathSciNet  MATH  Google Scholar 

  • de Larminat P (1980) Unconditional stabilizers for non minimum phase systems. In: Proc int symp on adaptive systems, Ruhr-University, Bochum

    Google Scholar 

  • de Larminat P (1984) On the stabilization condition in indirect adaptive control. Automatica 20:793–795

    Article  MathSciNet  MATH  Google Scholar 

  • de Larminat P (1986) Une solution robuste au problème de la stabilité dans la commande adaptative indirecte passive. In: Landau ID, Dugard L (eds) Commande adaptative: aspects pratiques et théoriques. Masson, Paris

    Google Scholar 

  • de Larminat P, Raynaud HF (1988) A robust solution to the admissibility problem in indirect adaptive control without persistency excitation. Int J Adapt Control Signal Process 2:95–110

    Article  MATH  Google Scholar 

  • Eliott H (1985) Global stability of adaptive pole placement algorithm. IEEE Trans Autom Control 30:348–356

    Article  Google Scholar 

  • Giri F, M’Saad M, Dion JM, Dugard L (1989) A globally convergent pole placement indirect adaptive controller. IEEE Trans Autom Control AC-34:353–356

    Article  MathSciNet  Google Scholar 

  • Giri F, M’Saad M, Dion JM, Dugard L (1990) A general lemma for the stability analysis of discrete-time adaptive control. Int J Control 51:283–288

    Article  MathSciNet  MATH  Google Scholar 

  • Giri F, M’Saad M, Dion JM, Dugard L (1991) On the robustness of discrete-time indirect adaptive (linear) controllers. Automatica 27:153–160

    Article  MathSciNet  MATH  Google Scholar 

  • Goodwin GC, Sin KS (1984) Adaptive filtering prediction and control. Prentice Hall, New York

    MATH  Google Scholar 

  • Goodwin GC, Teoh EK (1985) Persistency of excitation in presence of possibly unbounded signals. IEEE Trans Autom Control AC-30:595–597

    Article  MathSciNet  Google Scholar 

  • Guo L (1996) Self-convergence of weighted least squares with applications to stochastic adaptive control. IEEE Trans Autom Control AC-41(1):79–89

    Google Scholar 

  • Kailath T (1980) Linear systems. Prentice-Hall, New York

    MATH  Google Scholar 

  • Kreisselmeier G (1986) A robust indirect adaptive control approach. Int J Control 43:161–175

    Article  MATH  Google Scholar 

  • Kreisselmeier G, Smith MC (1986) Stable adaptive regulation of arbitrary nth order plants. IEEE Trans Autom Control AC-31:299–305

    Article  MathSciNet  Google Scholar 

  • Lam K (1982) Design of stochastic discrete-time linear optimal control. Int J Syst Sci 13(19):979–1011

    Article  MATH  Google Scholar 

  • Lancaster P, Tismenetsky M (1985) The theory of matrices, 2nd edn. Academic Press, New York

    MATH  Google Scholar 

  • Landau ID, Karimi A (1997b) Recursive algorithms for identification in closed loop: a unified approach and evaluation. Automatica 33(8):1499–1523

    Article  MathSciNet  MATH  Google Scholar 

  • Landau ID, Rey D, Karimi A, Voda-Besançon A, Franco A (1995a) A flexible transmission system as a benchmark for robust digital control. Eur J Control 1(2):77–96

    Google Scholar 

  • Langer J, Landau ID (1999) Combined pole placement/sensitivity function shaping method using convex optimization criteria. Automatica 35(6):1111–1120

    Article  MathSciNet  MATH  Google Scholar 

  • Lozano R (1989) Robust adaptive regulation without persistent excitation. IEEE Trans Autom Control AC-34:1260–1267

    Article  Google Scholar 

  • Lozano R (1992) Singularity-free adaptive pole placement without resorting to persistency of excitation detailed analysis for first order systems. Automatica 28:27–33

    Article  MathSciNet  MATH  Google Scholar 

  • Lozano R, Goodwin GC (1985) A globally convergent pole-placement algorithm without persistency of excitation requirement. IEEE Trans Autom Control AC-30:795–797

    Article  Google Scholar 

  • Lozano R, Zhao X (1994) Adaptive pole placement without excitation probing signals. IEEE Trans Autom Control AC-39(1):47–58

    Article  MathSciNet  Google Scholar 

  • Lozano R, Dion JM, Dugard L (1993) Singularity-free adaptive pole placement for second order systems. IEEE Trans Autom Control AC-38:104–108

    Article  MathSciNet  Google Scholar 

  • Mareels I, Polderman JW (1996) Adaptive systems: an introduction. Birkhauser, Basel

    MATH  Google Scholar 

  • Middleton RH, Goodwin GC, Hill DJ, Mayne DQ (1988) Design issues in adaptive control. IEEE Trans Autom Control AC-33(1):50–58

    Article  MathSciNet  Google Scholar 

  • M’Saad M, Chebassier J (1997) Simart: un progiciel pour l’automatique et ses applications. In: Proc des journées d’études sur les logiciels, Nancy, France

    Google Scholar 

  • M’Saad M, Sanchez G (1992) Partial state model reference adaptive control of multivariable systems. Automatica 28(6):1189–1194

    Article  MathSciNet  MATH  Google Scholar 

  • M’Saad M, Dugard L, Hammad S (1993a) A suitable generalized predictive adaptive controller case study: control of a flexible arm. Automatica 29(3):589–608

    Article  MathSciNet  MATH  Google Scholar 

  • M’Saad M, Giri F, Dion JM, Dugard L (1993b) Techniques in discrete time robust adaptive control. In: Leondes CT (ed) Control and dynamical systems, vol 56. Academic Press, San Diego, pp 93–161

    Google Scholar 

  • Ossman KA, Kamen ED (1987) Adaptive regulation of MIMO linear discrete-time systems without requiring a persistent excitation. IEEE Trans Autom Control AC-32:397–404

    Article  MathSciNet  Google Scholar 

  • Polderman JW (1989) A state space approach to the problem of adaptive pole assignment. Math Control Signals Syst 2(1):71–94

    Article  MathSciNet  MATH  Google Scholar 

  • 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 AC-30(9):881–889

    Article  Google Scholar 

  • Samson C (1982) An adaptive LQ controller for non-minimum phase systems. Int J Control 3:389–397

    MathSciNet  MATH  Google Scholar 

  • Visual Solutions (1995) Vissim—User manual, version 2.0. Westford, MA, USA

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ioan Doré Landau .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag London Limited

About this chapter

Cite this chapter

Landau, I.D., Lozano, R., M’Saad, M., Karimi, A. (2011). Indirect Adaptive Control. In: Adaptive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-664-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-0-85729-664-1_12

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-663-4

  • Online ISBN: 978-0-85729-664-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics