Abstract
We present a method for computing the optimal level of performance for the H ∞ optimal mixed sensitivity problem for systems described by irrational transfer functions when the plant is a stable transfer function (an H ∞ function), and an explicit inner/outer factorization of the plant is not available. This technique is applicable to plants for which the only available frequency response information consists of test data. We discuss some numerical issues and illustrate with an application.
This research has been partially supported by the U.S. Air Force Office of Scientific Research under grants no. AFOSR-89-0205 and AFOSR-91-0231, and by a National Science Foundation Graduate Fellowship award.
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References
D.S. Flamm, “A Model of a Damped Flexible Beam,” ISS Report No. 54, Princeton University Dept. of Electrical Engineering, June 14, 1990.
D.S. Flamm and K.M. Klipec, “Numerical Computation of H ∞-Optimal Performance for Feedback Control Systems and Well-Posedness of Optimality Criteria,” submitted to Proc. 31st IEEE Conf. on Decision and Control.
D.S. Flamm and H. Yang, “H ∞-Optimal Mixed Sensitivity for General Distributed Plants,” Proc. 29th IEEE Conf. on Decision and Control, Honolulu, HI, Dec. 5–7, 1990, pp. 134–139.
K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, 1962.
K. Klipec, “Derivations of Transfer Functions for Beam Models”, September 4, 1990.
R. Piessens, et al., QUADPACK, A Subroutine Package for Automatic Integration, Springer-Verlag, 1983.
Y. Sakawa and Z-H Luo, “Modeling and Control of Coupled Bending and Torsional Vibrations of Flexible Beams,” IEEE Trans. Automatic Control, 34(9), Sept. 1989, pp. 970–977.
M.C. Smith, “Well-Posedness of H ∞ Optimal Control Problems,” SIAM J. Control and Optimization, 28(2), March 1990, pp. 342–358.
G. Zames and S.K. Mitter, “A Note on Essential Spectra and Norms of Mixed Hankel-Toeplitz Operators,” Systems and Control Letters, 10, 1988, pp. 159–165.
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© 1993 Springer-Verlag
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Flamm, D.S., Klipec, K. (1993). Numerical methods for H ∞ control of distributed parameter systems. In: Curtain, R.F., Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. Lecture Notes in Control and Information Sciences, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0115057
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DOI: https://doi.org/10.1007/BFb0115057
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