Journal of Mechanical Science and Technology

  • 제14권2호
  • /
  • Pages.168-176
  • /
  • 2000
  • /
  • 1738-494X(pISSN)
  • /
  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

Model Reference Adaptive Control of a Time-Varying Parabolic System

  • Hong, Keum-Shik (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Yang, Kyung-Jinn (Department of Mechanical and Intelligent Systems Engineering Graduate College, Pusan National University) ;
  • Kang, Dong-Hunn (Department of Mechanical and Intelligent Systems Engineering Graduate College, Pusan National University)
  • 발행 : 2000.02.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

키워드

참고문헌

  1. Anderson, B. D. O., Bitmead, R. R., Johnson, C. R., Jr., Kokotovic, P. V., Kosut, R. L., Mareels, I. M. Y., Praly, L., and Riedle, B. D., 1986, Stability of Adaptive Systems : Passivity and Averaging Analysis. MIT Press, Cambridge, MA
  2. Astrom, K., and Wittenmark, B., 1995, Adaptive Control, Addison-Wesley, Reading, MA
  3. Balas, M. J., 1983, 'Some Critical Issues in Stable Finite Dimensional Adaptive Control of Linear Distributed Parameter System,' Proc. 4th Yale Conf. Adaptive Control
  4. Banks, H. T., and Kunisch, K., 1989, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston
  5. Baumeister, J., and Scondo, W., 1987, 'Asymptotic Embedding Methods for Parameter Estimation,' in Proc. 26th IEEE Conf. Dec. Contr., Los Angeles, CA, pp. 170-174 https://doi.org/10.1109/CDC.1987.272735
  6. Baumeister, J., Scondo, W., Demetriou, M. A., and Rogen I. G., 1997, 'On-Line Parameter Estimation for Infinite-Dimensional Dynamical Systems,' SIAM J. Control Optim., Vol. 35, No. 2, pp. 678-713 https://doi.org/10.1137/S0363012994270928
  7. Bentsman, J., Solo, V., and Hong, K. S., 1992, 'Adaptive Control of A Parabolic System with Time Varying Parameters : Averaging Analysis,' Proceedings of the 31st IEEE CDC, pp. 710-711
  8. Corless, M. J., and Leitmann, G., 1981, 'Continuous State Feedback Guaranteeing Uniform Boundedness for Uncertain Dynamic Systems,' IEEE Trans. Automat. Contr., Vol. 26, No.5, pp. 1139-1144 https://doi.org/10.1109/TAC.1981.1102785
  9. Demetriou, M. A., and Rosen, I. G., 1994, 'On the Persistence of Excitation in the Adaptive Estimation of Distributed Parameter Systems,' IEEE Trans, Automat. Contr., Vol. 39, No. 5, pp. 1117-1123 https://doi.org/10.1109/9.284907
  10. Henry, D., 1981, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag
  11. Hong, K. S., and Bentsman, J., 1992, 'Nonlinear Control of Diffusion Processes with Uncertain Parameters Using MRAC Approach,' Proceedings American Control Conference, Chicago, IL, pp. 1343-1347
  12. Hong, K. S., and Bentsman, J., 1994a, 'Direct Adaptive Control of Parabolic Systems : Algorithm Synthesis, Convergence and Stability Analysis,' IEEE Trans. Automat. Contr., Vol. 39, No. 10, pp. 2018-2033 https://doi.org/10.1109/9.328823
  13. Hong, K. S., and Bentsman, J., 1994b, 'Application of Averaging Method for Integro -Differential Equations to Model Reference Adaptive Control of Parabolic Systems,' Automatica, Vol. 30, No. 9, pp. 1415-1419 https://doi.org/10.1016/0005-1098(94)90006-X
  14. Hong, K. S., Wu, J., and Lee, K. I., 1994, 'New Conditions for the Exponential Stability of Evolution Equations,' IEEE Trans. Automat. Contr., Vol. 39, No. 7, pp. 1432-1436 https://doi.org/10.1109/9.299627
  15. Hong, K. S., 1997, 'Asymptotic Behavior Analysis of a Coupled Time-Varying System : Application to Adaptive Systems,' IEEE Trans. Automat. Contr., Vol. 42, No. 12, pp. 1693-1697 https://doi.org/10.1109/9.650018
  16. Kobayashi, T., 1988, 'Finite Dimensional Adaptive Control for Infinite Dimensional Systems,' Int. J. Contr., Vol. 48, No. 1, pp. 289-302 https://doi.org/10.1080/00207178808906175
  17. Middleton, R. H., and Goodwin, G. C., 1988, 'Adaptive Control of Time Varying Linear Plants,' IEEE Trans. Automat. Contr., Vol. 33, pp.150-155 https://doi.org/10.1109/9.382
  18. Miyasato, Y., 1990, 'Model Reference Adaptive Control for Distributed Parameter Systems of Parabolic Type by Finite Dimensional Controller,' Proc. 29th IEEE CDC, Honolulu, pp. 1459-1464 https://doi.org/10.1109/CDC.1990.203853
  19. Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems, Prentice Hall
  20. Pazy, A., 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York
  21. Sastry, S., and Bodson, M., 1989, Adaptive Control: Stability, Convergence and Robustness, Prentice Hall
  22. Solo, V., 1996, 'Deterministic Adaptive Control with Slowly Varying Parameters : An Averaging Analysis,' Int. J. Control, Vol. 64, No. 1, pp. 99-125 https://doi.org/10.1080/00207179608921619
  23. Tsakalis, K. S., and Ioannou, P. A., 1993, Linear Time-Varying Systems : Control and Adaptation, Prentice Hall
  24. Walker, J. A., 1980, Dynamical Systems and Evolution Equations, New York, Plenum Press