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Nonlinear boundary control of coupled Burgers' equations

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Języki publikacji
EN
Abstrakty
EN
This paper is concerned with adaptive stabilization of two coupled viscous Burgers' equations by nonlinear boundary controllers. Under the existence of bounded deterministic disturbances, the adaptive controllers are constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the controlled system the global stability and the convergence of the system states to zero will be guaranteed. It is shown that the theory can be generalized to the systems with higher-order nonlinearity.
Rocznik
Strony
245--258
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Department of Mechanical and Control Engineering Faculty of Engineering, Kyushu Institute of Technology Tobata, Kitakyushu 804-8550, Japan
autor
  • Department of Mechanical and Control Engineering Faculty of Engineering, Kyushu Institute of Technology Tobata, Kitakyushu 804-8550, Japan
Bibliografia
  • BOHM, M., DEMETRIOU, M.A., REICH, S. and ROSEN, I. G. (1998) Model reference adaptive control of distributed parameter systems. SIAM J. Control Optim. 36 33- 81.
  • BURNS, J.A., and KANG, S. (1991) A control problem for Burgers' equation with bounded input-output. Nonlinear Dynamics, 2, 235- 262.
  • BYRNES, C. I., GILLIAM, D.S., and SHUBOV, V.I. (1998) On the global dynamics of a controlled viscous Burgers' equation. J. Dynam. Control Systems 4 , John Wiley and Sons, Inc., 457-519.
  • CURTAIN, R .F ., and ZWART, H.J. (1995) An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, Berlin-New York.
  • FARLOW, S.J. (1982) Partial Differential Equations for Sientists and Engineers. John Wiley and Sons, Inc.
  • HABERMAN, R. (1977) Mathematical Models in Mechanical Vibrations, Population Dynamics, and Traffic Flow. Prentice Hall, Inc.
  • HENRY, D . (1981) Geometric theory of semilinear paraboloc equations. Springer Verlag, Berlin-New York.
  • ITO, K., and YAN, Y. (1998) Viscous scalar conservation laws with nonlinear flux feedback and global attractors. J. Math. Anal. Appl., 227, 271-299.
  • KOBAYASHI, T. (1987) Global adaptive stabilization of infinite dimensional systems. Systems and Control Letters, 9, 215- 223.
  • KOBAYASHI, T. (1988) Finite dimensional adaptive control for infinite dimensional systems. Int. J. Control, 48, 289-302.
  • KOBAYASHI, T. (1996) High-gain adaptive stabilization of collocated distributed parameter systems. Archives of Control Sciences, 5{XLI), 87-97.
  • KOBAYASHI, T ., 0YA, M., and FAN, J. (1997) Adaptive regulator design for collocated parabolic distributed parameter systems. Trans. of ISCIE, 10, 70- 77.
  • KOBAYASHI, T. (2001) Adaptive regulator design of a viscous Burgers' system by boundary control. IMA J. of Mathematical Control and Information, 18, 427- 437.
  • KRSTIC, M. (1999) On global stabilization of Burgers' equation by boundary control. Systems and Control Letters, 37, 123-141.
  • LIU, W.J., and KRSTIC, M. (2000) Backstepping boundary control of Burgers' equation with actuator dynamics. Systems and Control Letters, 4 1, 291- 303.
  • BALOGH, A., and KRSTIC, M. (2000) Burger's equation with nonlinear boundary feedback: H 1 stability, well-posed-ness and simulation. Mathematical Problems in Engineering, 6, 189- 200.
  • LIU, W .J., and KRSTIC, M. (2001) Adaptive control of Burger's equation with unknown viscosity. Int. J. of Adaptive Control and Signal Processing, 15, 745- 766.
  • LOGEMANN, H., and MARTENSSON, B. (1992) Adaptive stabilization of infinitedimensional systems. IEEE Trans. on Automatic Control, 37, 1869-1883.
  • LOGEMANN, H., and TOWNLEY, S. (1997) Adaptive control of infinite-dimensional systems without parameter estimation: an overview. IMA J. of Mathematical Control and Information, 14, 175- 206.
  • Luo, Z-H., Guo, B-Z., and MoRGUL, 0. (1999) Stability and Stabilization of Infinite Dimensional Systems with Applications. Springer-Verlag, London.
  • TEMAM, R. (1997) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York.
  • VAN LY, H., MEASE, K. D., and TITI, E.S. (1997) Distributed and boundary control of the viscous Burgers' equation. Numer. Funct. Anal. Optim., 18, 143-188.
  • WEN, J.T., and BALAS, M.J. (1989) Robust adaptive control in Hilbert space. J. of Mathematical Analysis and Applications, 143, 1-26.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0006
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