New efficient frequency domain algorithm for H∞ approximation with applications to controller reduction

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New efficient frequency domain algorithm for H∞ approximation with applications to controller reduction

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New frequency domain computational schemes for the weighted and unweighted H∞ norm system approximation problems are introduced. The schemes are applicable in both continuous and discrete-time cases. The new algorithm is used to obtain reduced order controllers for a well known control problem.

Inspec keywords: H∞ optimisation; H∞ control; reduced order systems; discrete time systems; continuous time systems; frequency-domain analysis; transfer functions

Other keywords: frequency domain algorithm; transfer function; continuous systems; discrete-time systems; controller reduction; H infinity norm approximation; reduced order controllers

Subjects: Discrete control systems; Optimal control; Control system analysis and synthesis methods; Optimisation techniques

References

    1. 1)
      • LAWSON, C.L.: `Contributions to the theory of linear least maximum approximation', 1961, PhD thesis, University of California.
    2. 2)
      • K. ZHOU , J.C. DOYLE , K. GLOVER . (1996) , Robust and optimal control.
    3. 3)
      • KAVRANOĞLU, D., BETTAYEB, M.: `LMI based computational schemes for ', Proceedings of 13th IFAC world congress, 1996, San Francisco, USA.
    4. 4)
      • S. ELLACOTT , J. WILLIAMS . Linear Chebyshev approximation in complex plane using Lawson's algorithm. Math. Comput. , 35 - 44
    5. 5)
      • GODDARD, P.J., GLOVER, K.: `Performance preserving frequency weighted controller approximation: A coprime factorisation approach', Proceedings of CDC 94, 1994, Lake Buena Vista, FL, p. 2720–2725.
    6. 6)
      • D. KAVRANOĞLU , M. BETTAYEB . Characterisation of the solution to the optimal H∞ model reduction problem. Syst. Control Lett. , 99 - 107
    7. 7)
      • B.C. MOORE . Principal component analysis in linear systems: Controllability, observability and model reduction. IEEE Trans. Autom. Control , 17 - 31
    8. 8)
      • GODDARD, P.J., GLOVER, K.: `Controller reduction: Weights for stability and performance preservation', Proceedings of CDC 93, 1993, San Antonio, Texas, p. 2903–2908.
    9. 9)
      • J. WILLIAMS . Characterisation and computation of rational Chebyshev approximations in the complex plane. SIAM J. Numer. Anal. , 819 - 827
    10. 10)
      • J.R. RICE . (1969) , The approximation of functions. Vol. II: Nonlinear and multivariate theory.
    11. 11)
      • ENNS, D.: `Model reduction for control system design', 1984, PhD thesis, Stanford University, Aeronautics and Astronautics Department.
    12. 12)
      • H.L. LOEB . Algorithms for Chebyshev approximations using the ratio of linear forms. J. Soc. Ind. Appl. Math. , 458 - 465
    13. 13)
      • LOEB, H.L.: `On rational fraction approximations at discrete points'. Convair Astronautics, Math. Preprint no. 9', 1957.
    14. 14)
      • KAVRANOĞLU, D., AHMED, M.S.: ` norm approximation by identification techniques', Proceedings of CDC 95, 1995, New Orleans, USA, p. 796–801.
    15. 15)
      • KAVRANOĞLU, D.: `Computation of the solution for the optimal ', Proceedings of ACC 93, 1993, San Francisco, p. 2190–2194.
    16. 16)
      • S. ELLACOTT , J. WILLIAMS . Rational Chebyshev approximation in the complex plane. SIAM J. Numer. Anal. , 310 - 323
    17. 17)
      • C.M. LEE , F.D.K. ROBERTS . A comparison of algorithms for rational l∞ approximation. Math. Comput. , 111 - 121
    18. 18)
      • G.A. LATHAM , B.D.O. ANDERSON . Frequency weighted optimal Hankel-norm approximation of stable transfer function. Syst. Control Lett. , 229 - 236
    19. 19)
      • G. BALAS , J.C. DOYLE , K. GLOVER , A. PACKARD , R. SMITH . (1991) , μ-analysis and synthesis toolbox.
    20. 20)
      • E. HAYASHI , L.N. TREFETHEN , M.H. GUTKNECHT . The CF table. Constr. Approx. , 195 - 223
    21. 21)
      • KAVRANOĞLU, D.: `Controller reduction for uncertain systems', Proceedings of CDC 96, 1996, Kobe, Japan, p. 887–892.
    22. 22)
      • KAVRANOĞLU, D.: `Elementary solutions for the ', 1989, PhD thesis, California Institute of Technology, Electrical Engineering Department.
    23. 23)
      • K. Glover . All optimal Hankel-norm approximations of linear multivariable systems and their L∞ error bounds. Int. J. Control , 1115 - 1193
    24. 24)
      • B.D.O. ANDERSON , Y. LIU . Controller reduction: Concepts and approaches. IEEE Trans. Autom. Control , 802 - 812
    25. 25)
      • L.N. TREFETHEN . (1983) Chebyshev approximation on the unit disk, Computational aspects of complex analysis.
    26. 26)
      • KAVRANOĞLU, D., AL-AMER, S.H.: `A new frequency domain technique for ', Proceedings of CDC 96, 1996, Kobe, Japan, p. 4574–4579.
    27. 27)
      • YANG, X.H., PACKARD, A.: `A low order controller design method', Proceedings of CDC 95, 1995, p. 3068–3073.
    28. 28)
      • V.R. ALGAZI , M. SUK , C.-S. RIM . Design of almost minimax filters in one and two dimensions by WLS techniques. IEEE Trans. Circuits Syst. , 590 - 596
    29. 29)
      • K. Zhou . Frequency-weighted L∞ norm and optimal Hankel norm model reduction. IEEE Trans. Autom. Control , 10 , 1687 - 1699
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