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A conceptual framework for parameter adaptive control

  • Part I Adaptive Linear Control
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Foundations of Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 160))

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Abstract

A conceptual framework is described in which a parameter adaptive control system is taken to be the feedback interconnection of a process Σ P and a parameterized controller Σ C(k) whose parameter vector k is adjusted by a tuner Σ T. The framework is general enough to encompass almost all parameterized controllers proposed in the literature for stabilizing linear process models. Emphasis is placed on the importance to adaptation of one of Σ C's outputs called a tuning error e T, which is the main signal driving Σ T. For the closed-loop parameterized system Σ(k) consisting of Σ P and Σ C(k), definitions and characterizations are given of the concepts of weak tunability and tunability of Σ(k) on a subset ɛ of the parameter space p in which k takes values. It proves to be necessary to know a subset ɛ on which Σ(k) is weakly tunable in order to be able to construct a tuner Σ T which adaptively stabilizes Σ(k). For a large class of linear multivariable process models, a properly designed certainty equivalence controller results in a tunable closed-loop parameterized system. The importance of this result to both the analysis and synthesis of parameter adaptive control systems is discussed. It is demonstrated by means of examples how the connection between certainty equivalence and tunability, together with the concept of tunability itself, can be used to markedly simplify the stability analysis of adaptive control systems. A new family of indirect parameterized controllers is described which have capabilities comparable to those of the well-known direct parameterized controllers which for a long time have served as basic building blocks for adaptive control systems of all types. The concept of implicit tuning is formalized and its potential importance to adaptive control is briefly discussed.

This research was supported by the National Science Foundation under grant ECS-9012551.

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References

  1. A. S. Morse, “Towards a unified theory of parameter adaptive control-tunability,” IEEE Trans. Aut. Control, vol. AC-35, pp. 1002–1012, Sept. 1990.

    Google Scholar 

  2. A. S. Morse, “Towards a unified theory of parameter adaptive control-Part 2: certainty equivalence and implicit tuning,” IEEE Trans. Aut. Control, to appear.

    Google Scholar 

  3. A. Feuer and A. S. Morse, “Adaptive control of single-input single-output linear systems,” IEEE Trans. Aut. Control, vol. AC-23, pp. 557–569, Aug. 1978.

    Google Scholar 

  4. A. S. Morse, “Global stability of parameter-adaptive control systems,” IEEE Trans. Aut. Control, vol. AC-25, pp. 433–439, June 1980.

    Google Scholar 

  5. G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1984.

    Google Scholar 

  6. K. J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley Publishing Co., 1989.

    Google Scholar 

  7. K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1989.

    Google Scholar 

  8. S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1989.

    Google Scholar 

  9. R. D. Nussbaum, “Some remarks on a conjecture in parameter adaptive control,” Syst. Control Lett., vol. 3, pp. 243–246, 1983.

    Google Scholar 

  10. B. Martensson, “The order of any stabilizing regulator is sufficient a priori information for adaptive stabilizing,” Syst. Control Lett., vol. 6, pp. 87–91, 1985.

    Google Scholar 

  11. A. S. Morse, “A three dimensional universal controller for the adaptive stabilization of any strictly proper minimum-phase system with relative degree not exceeding two,” IEEE Trans. Aut. Control, vol. AC-30, pp. 1188–1191, Dec. 1985.

    Google Scholar 

  12. J. C. Willems and C. I. Byrnes, “Global adaptive stabilization in the absence of information on the sign of the high-frequency gain,” Lecture Notes in Control and Information Sciences, Proc. 6th Int. Conf. on Analysis and Optimization of Systems, Nice, June 1984, pp. 49–57.

    Google Scholar 

  13. D. E. Miller, Adaptive Control of Uncertain Systems, Doctoral Thesis, University of Toronto, Oct. 1989.

    Google Scholar 

  14. M. A. Duarte and K. S. Narendra, “Combined direct and indirect approach to adaptive control,” Center for Systems Science, Yale University, Report No. 8711, Sept. 1987.

    Google Scholar 

  15. J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, 1969.

    Google Scholar 

  16. G. Kreisselmeier, “An approach to stable indirect adaptive control,” Automatica, vol. 21, pp. 425–431, July 1985.

    Google Scholar 

  17. R. H. Middleton, G. C. Goodwin, D. J. Hill and D. Q. Mayne, “Design Issues in Adaptive Control,” IEEE Trans. Aut. Control, vol. 33, pp. 50–58, Jan. 1988.

    Google Scholar 

  18. F. Pait and A. S. Morse, “A smoothly parameterized family of stabilizable, observable linear systems containing realizations of all transfer functions of McMillan degree not exceeding n,” IEEE Trans. Aut. Control, to appear.

    Google Scholar 

  19. P. Ioannou and J. Sun, “Theory and design of robust direct and indirect adaptive-control schemes,” Int. J. Control, vol. 47, pp. 775–813, 1988.

    Google Scholar 

  20. B. Egardt, Stability of Adaptive Controllers, Springer-Verlag, Lecture Notes in Control and Information Sciences, vol. 20, 1979.

    Google Scholar 

  21. L. Praly, “Global stability of direct adaptive control schemes with respect to a group topology,” Adaptive and Learning Systems, Plenum Press, 1986, pp. 1009–1014.

    Google Scholar 

  22. B. D. O. Anderson and R. M. Johnstone, “Global adaptive pole positioning,” IEEE Trans. Aut. Control, vol. AC-30, pp. 11–22, Jan. 1985.

    Google Scholar 

  23. A. S. Morse, “Structural invariants of linear multivariable systems,” SIAM J. Control, vol. 11, pp. 446–465, Aug. 1973.

    Google Scholar 

  24. R. V. Monopoli, “Model reference adaptive control with an augmented error signal,” IEEE Trans. Aut. Control, vol. AC-19, pp. 474–484, Oct. 1974.

    Google Scholar 

  25. L. Praly, “Towards a globally stable direct adaptive control scheme for not necessarily minimum phase systems,” IEEE Trans. Aut. Control, vol. AC-29, pp. 946–949, Oct. 1984.

    Google Scholar 

  26. S. Dasgupta and B. D. O. Anderson, “Physically based parameterizations for the design of adaptive controllers,” Dept. of Systems Eng. Report, Australian National University, Canberra, 1986.

    Google Scholar 

  27. A. S. Morse, “Indirect adaptive control of processes satisfying the classical assumptions of direct adaptive control,” Proc. 1988 Amer. Control Conf., Atlanta, GA.

    Google Scholar 

  28. A. S. Morse, D. Q. Mayne and G. C. Goodwin, “Identifier-based, switched-parameter algorithms for the adaptive stabilization of linear systems,” Proc. Sixth Yale Workshop on Adaptive and Learning Systems, New Haven, Aug. 1990.

    Google Scholar 

  29. G. Kreisselmeier and M. C. Smith, “Stable adaptive regulation of arbitrary nthorder plants,” IEEE Trans. Aut. Control, vol. AC-31, pp. 299–305, April 1986.

    Google Scholar 

  30. H. Elliot, “Direct adaptive pole placement with application to nonminimum phase systems,” IEEE Trans. Aut. Control, vol. AC-27, pp. 720–722, June 1982.

    Google Scholar 

  31. C. R. Johnson, Jr., Lectures on Adaptive Parameter Estimation, Prentice-Hall, Inc., 1987.

    Google Scholar 

  32. G. Bastin and M. R. Gevers, “Stable adaptive observers for nonlinear time-varying systems,” IEEE Trans. Aut. Control, vol. AC-33, pp. 650–658, July 1988.

    Google Scholar 

  33. A. S. Morse and W. M. Wonham, “Status of non-interacting control,” IEEE Trans. Aut. Control, vol. AC-16, pp. 568–581, Dec. 1971.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Yale University, P. O. Box 1968, 06520-1968, New Haven, CT, USA

    A. S. Morse

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  1. A. S. Morse
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Petar V. Kokotović

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© 1991 Springer-Verlag

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Morse, A.S. (1991). A conceptual framework for parameter adaptive control. In: Kokotović, P.V. (eds) Foundations of Adaptive Control. Lecture Notes in Control and Information Sciences, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044773

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  • DOI: https://doi.org/10.1007/BFb0044773

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54020-5

  • Online ISBN: 978-3-540-47351-0

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