Adaptive Control of a Family of Plants

  • D. E. Miller
  • E. J. Davison
Part of the Progress in Systems and Control Theory book series (PSCT, volume 6)


Consider a linear time-invariant (LTI) plant which is not completely specified, but instead belongs to a finite set of known plants, say {P i : ip}. Our objective is to design a controller which provides “good” tracking and disturbance rejection, in a sufficiently well-defined sense, for this partially known plant. We first design a high-performance LTI controller K i for each possible P i if the pair (P i , K j ) is stable iff i = j and has no eigenvalues on the imaginary axis for any i, jp and if an upper bound on the magnitude of the unmeasurable disturbance signal is available, then it is shown that a switching mechanism can be used to find the correct LTI controller; furthermore, each LTI controller need only be tried once. This kind of problem often arises in an industrial setting, and is often approached using heuristic “gain-scheduling” techniques.


Adaptive Control Close Loop System Imaginary Axis Loop System Disturbance Rejection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    B. Mârtensson, “The Order of any Stabilizing Regulator is Sufficient a priori Information for Adaptive Stabilization”, Syst. Contr. Lett, pp 87–91, July 1985.Google Scholar
  2. [2]
    D. E. Miller and E.J. Davison, “An Adaptive Controller which can Stabilize any Stabilizable and Detectable LTI System”, Analysis and Control of Nonlinear Systems, (editors: C.I. Byrnes, C.F. Byrnes, R.E. Saeks ), North-Holland, 1988, pp. 51–58.Google Scholar
  3. [3]
    M. Fu and B.R. Barmish, “Adaptive Stabilization of Linear Systems via Switching Control”, IEEE Trans. Automat. Contr, vol. AC-31, pp. 1097–1103, Dec. 1986.Google Scholar
  4. [4]
    D.E. Miller and E.J. Davison, “An Adaptive Controller Which Provides Lyapunov Stability”, IEEE Trans. Automat. Contr, vol. AC-34, pp. 599–609, June 1989.Google Scholar
  5. [5]
    B. Mârtensson, “Adaptive Stabilization Without High-Gain”, in Proc. IIASA Conf, July 1986 (Lecture Notes in Control and Information Sciences, Vol. 105 ). New York: Springer-Verlag, 1988, pp. 226–238.Google Scholar
  6. [6]
    D.E. Miller and E.J. Davison, “A New Self-Tuning Controller to Solve the Servomechanism Problem”, Proc. of the 26th CDC, Dec. 1987, pp. 843–849.Google Scholar
  7. [7]
    E.J. Davison and A. Goldenberg, “Robust Control of a General Problem: The Servocompensator”, Automatica, vol. 11, pp 461–471.Google Scholar
  8. [8]
    E.J. Davison and S.H. Wang, “Properties and Calculation of Transmission Zeros of Linear Multivariable Systems”, Automatica, vol. 10, pp 643–658, Dec. 1974.Google Scholar
  9. [9]
    E.J. Davison and I. Ferguson, “The Design of Controllers for the Multivariable Robust Servomechanism Problem Using Parameter Optimization Methods”, IEEE Trans. Autom. Contr, vol. 26, pp. 93–110, Feb. 1981.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • D. E. Miller
    • 1
  • E. J. Davison
    • 1
  1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada

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