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Some remarks on adaptive stabilization of infinite-dimensional second order systems

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Języki publikacji
EN
Abstrakty
EN
In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case of the input and output operators being collocated. The advantage of the adaptive law is that good control performance can be automatically achieved even in the presence of various types of uncertainties. The adaptive stabilizer is constructed by the concept of high-gain output feedback. An energy-like function and a multiplier function are introduced and adaptive stabilization of the linear second order systems is analyzed. It is shown that the theory of adaptive stabilization can be also applied to some nonlinear systems.
Rocznik
Strony
5--16
Opis fizyczny
Bibliogr. 18 poz., wzory
Twórcy
autor
  • Department of Mechanical and Control Engineering, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Japan
Bibliografia
  • [1] G. Chen, M. C. Delfour, A. M. Krall and G. Payre: Modeling, stabilization and control of serially connected beams. SIAM J. Control and Optimization, 25 (1987), 526-546.
  • [2] R. F. Curtain and P. J. Pritchard: Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, 8 Springer, Berlin-New York, 1978.
  • [3] R. F. Curtain, and H.J. Zwart: An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, Berlin-New York, 1995.
  • [4| T. Kobayashi: Global adaptive stabilization of infinite dimensional systems.Systems and Control Letters, 9 (1987), 215-223.
  • [5] T. Kobayashi: Finite dimensional adaptive control for infinite dimensional systems. Int. J. Control, 48 (1988), 289-302.
  • [6] T. Kobayashi: Zeros and design of control systems for distributed parameter systems. Int. J. Systems Sciense, 23 (1992), 1509-1515.
  • [7] T. Kobayashi: Hign-gain adaptive stabilization of collocated distributed parameter systems.Arcliives of Control Sciences, 5(XLI), (1996), 87-97.
  • [8] T. Kobayashi, M. Oya and J. Fan: Adaptive regulator design for collocated parabolic distributed parameter systems. Trans. Of ISCIE, 10 (1997), 70-77.
  • [9] J. L. Lions: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin, 1971.
  • [10] H. Logemann and H. Zwart:Some remarks on adaptive stabilization of infinitedimensional systems.Systems and Control Letters. 16 (1991) 199-207.
  • [11] H. Logemann and B. Martensson: Adaptive stabilization of infinitedimensional systems. IEEE Trans. on Automatic Control, 37 (1992), 1869-1883.
  • [12] Z-H Luo, B-Z Guo and O. Morgue: Stability and Stabilization of Infinite Dimensional Systems with Applications. Springer-Verlag, London, 1999.
  • [13] A. Pazy: Semigroups of Linear Operators and Applications lo Partial Differential Equations. Springer-Verlag, New York, 1983.
  • [14] R. Rebarber and S. Townley: Robustness and continuity of the spectrun for uncertain distributed parameter systems. Automatica, 31 (1995), 1533-1546.
  • [15] S. M. Shahruz:Boundary control of Kirchhoff's non-linear string. Int. J. Control, 72 (1999), 560-563.
  • [16] R. Teman: Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 1997.
  • [17] S. Townley: Simple adaptive stabilization of output feedback stabilizable distributed parameter systems. Dyn. Control 5 (1995), 107-123.
  • [18] J. T. Wen and M. J. Balas: Robust adaptive control in Hilbert space. J. of Mathematical Analysis and Applications, 143 (1989), 1-26.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW9-0009-1793
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