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An adaptive control for globally stabilizing linear systems with unknown high-frequency gains

  • Session 2 Stability I
  • Conference paper
  • First Online:
Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 62))

Abstract

This paper presents an algorithm for adaptively controlling a single-input, single-output process admitting an n-dimensional, minimum phase linear model of relative degree 1 or 2, with unknown parameters. Apriori knowledge of the sign of the model's high frequency gain is not required, and a sufficiently rich probing signal is not needed for stabilization.

The work of the author was supported in part, by the National Science Foundation, Grant No. ECS7916871; portions of this work were done while the author was visiting the Department of Electrical Engineering, University of Southern California, Los Angeles, California.

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References

  1. A. S. Morse, "Global Stability of Parameter-Adaptive Control Systems," IEEE Trans. Auto. Control, AC-25(3), June 1980, pp. 433–439.

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  2. K. S. Narendra, Y. H. Lin, L. S. Valavani, "Stable Adaptive Controller Design, Part II: Proof of Stability," ibid, pp. 440–448.

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  3. A. S. Morse, "Recent Problems in Parameter Adaptive Control," Proc. CNRS Colloquium on Development and Utilization of Mathematical Models in Automatic Control," Belle-Isle, France, Sept. 1982.

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  4. R. D. Nussbaum, "Some Remarks on a Conjecture in Parameter Adaptive Control," Systems and Control Letters, to appear.

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  5. J. C. Willems and C. I. Byrnes, "Global Adaptive Stabilization in the Absence of Information on the Sign of the Instantaneous Gain," Sixth Int. Conf. on the Analysis and Optimization of Systems, Nice, June 1984, to appear.

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  6. A. Feuer and A. S. Morse, "Adaptive Control of a Single-Input, Single-Output Linear System," IEEE Trans. Auto. Control, AC-23, Aug. 1978, pp. 557–569.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Yale University, 06520, New Haven, Ct., USA

    A. S. Morse

Authors
  1. A. S. Morse
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Editor information

A. Bensoussan J. L. Lions

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© 1984 Springer-Verlag

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Morse, A.S. (1984). An adaptive control for globally stabilizing linear systems with unknown high-frequency gains. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004945

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  • DOI: https://doi.org/10.1007/BFb0004945

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13551-7

  • Online ISBN: 978-3-540-39007-7

  • eBook Packages: Springer Book Archive

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