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2003 | 13 | 4 | 441-452
Tytuł artykułu

Adaptive compensators for perturbed positive real infinite-dimensional systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates, and the convergence of the estimator error. For the case of a known periodic exogenous input we design an adaptive compensator which forces the system to converge to a unique periodic solution. We illustrate our approach with a delay example and a diffusion example for which we obtain convincing numerical results.
Rocznik
Tom
13
Numer
4
Strony
441-452
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-09-05
poprawiono
2003-06-30
Twórcy
  • Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
  • Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA
autor
  • Center for Research in Scientific Computation, Box 8205 North Carolina State University, Raleigh, NC 276958205, USA
Bibliografia
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  • Curtain R.F. (1996a): Corrections to the Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. - Syst. Contr. Lett., Vol. 28, No. 4, pp. 237-238.
  • Curtain R.F. (1996b): The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems. - Syst. Contr. Lett., Vol. 27, No. 1, pp. 67-72.
  • Curtain R.F. (2001): Linear operator inequalities for stable weakly regular linear systems. - Math. Contr.Sign. Syst., Vol. 14, No. 4, pp. 299-337.
  • Curtain R.F., Demetriou M.A. and Ito K. (1997): Adaptive observers for structurally perturbed infinite dimensional systems. - Proc. IEEE Conf. Decision and Control, San Diego, California, pp. 509-514.
  • Curtain R.F. and Pritchard A.J. (1978): Infinite Dimensional Linear Systems Theory. - Berlin: Springer.
  • Curtain R.F. and Zwart H.J. (1995): An Introduction to Infinite Dimensional Linear Systems Theory. - Berlin: Springer.
  • Demetriou M.A., Curtain R.F. and Ito K. (1998): Adaptive observers for structurally perturbed positive real delay systems. - Proc. 4th Int. Conf. Optimization: Techniques and Applications, Curtin University of Technology, Perth, Australia, pp. 345-351.
  • Demetriou M.A. and Ito K. (1996): Adaptive observers for a class of infinite dimensional systems. - Proc. 13th World Congress, IFAC, San Francisco, CA, pp. 409-413.
  • Hansen S. and Weiss G. (1997): New results on the operator Carleson measure criterion. - IMA J. Math. Contr. Inf., Vol. 14, No. 1, pp. 3-32.
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  • Ito K. and Kappel F. (1991): A uniformly differentiable approximation scheme for delay systems using splines. - Appl. Math. Optim., Vol. 23, No. 3, pp. 217-262.
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  • Pandolfi L. (1997): The Kalman-Yacubovich theorem: An overview and new results for hyperbolic boundary control systems. - Nonlin. Anal. Theory Meth. Applic., Vol. 30, No. 30, pp. 735-745.
  • Pandolfi L. (1998): Dissipativity and Lur'e problem for parabolic boundary control systems. - SIAM J. Contr. Optim., Vol. 36, No. 6, pp. 2061-2081.
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  • Staffans O.J. (1997): Quadratic optimal control of stable well-posed linear systems. - Trans. Amer. Math. Soc., Vol. 349, No. 9, pp. 3679-3715.
  • Staffans O.J. (1998): Coprime factorizations and well-posed linear systems. - SIAM J. Contr. Optim., Vol. 36, No. 4, pp. 1268-1292.
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  • Titchmarsh E.C. (1962): Introduction to the Theory of Fourier Integrals. - New York: Oxford University Press.
  • Weiss M. (1994): Riccati Equations in Hilbert Spaces: A Popov Function Approach. - Ph.D. Thesis, Rijksuniversiteit Groningen, The Netherlands.
  • Weiss M. (1997): Riccati equation theory for Pritchard-Salamon systems: a Popov function approach. - IMA J. Math. Contr. Inf., Vol. 14, No. 1, pp. 45-83.
  • Weiss M. and Weiss G. (1997): Optimal control of stable weakly regular linear systems. - Math. Contr. Signals Syst., Vol. 10, No. 4, pp. 287-330.
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Bibliografia
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