Lyapunov adaptive stabilization of parabolic PDEs - Part I: A benchmark for boundary control

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 3164-3169

  Krstic, Miroslav ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEZOUT EQUATION; BOUNDARY CONTROL; PARAMETRIZED CONTROL FORMULA; PHYSICAL SYSTEMS;

ADAPTIVE SYSTEMS; CONTROL EQUIPMENT; LYAPUNOV METHODS; PRANDTL NUMBER; REYNOLDS NUMBER; RICCATI EQUATIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33847202939     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582648     Document Type: Conference Paper

References (32)

1. J. Bentsman and Y. Orlov, "Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types," Int. J. Adapt. Control Signal Process. vol. 15, pp. 679-696, 2001.
2. M. Bohm, M. A. Demetriou, S. Reich, and I. G. Rosen, "Model reference adaptive control of distributed parameter systems," SIAM J. Control Optim., Vol. 36, No. 1, pp. 33-81, 1998.
3. D. M. Boskovic and M. Krstic, "Stabilization of a solid propellant rocket instability by state feedback," Int. J. of Robust and Nonlinear Control, vol. 13, pp. 483-495, 2003.
4. M. S. de Queiroz, D. M. Dawson, M. Agarwal, and F. Zhang, "Adaptive nonlinear boundary control of a flexible link robot arm," IEEE Trans. Robotics and Automation, vol. 15, pp. 779-787, 1999.
5. M. A. Demetriou and K. Ito, "Optimal on-line parameter estimation for a class of infinite dimensional systems using Kalman filters," Proceedings of the American Control Conference, 2003.
6. T. E. Duncan, B. Maslowski, and B. Pasik-Duncan, "Adaptive boundary and point control of linear stochastic distributed parameter systems," SIAM J. Control Optim., vol. 32, no. 3, pp. 648-672, 1994.
7. K. S. Hong and J. Bentsman, "Direct adaptive control of parabolic systems: Algorithm synthesis, and convergence, and stability analysis," IEEE Trans. Automatic Control, vol. 39, pp. 2018-2033, 1994.
8. P. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, 1996.
9. M. Joavanovic and B. Bamieh, "Lyapunov-based distributed control of systems on lattices," IEEE Trans. Automatic Control, to appear.
10. T. Kobayashi, "Global adaptive stabilization of infinite-dimensional systems," Systems and Control Letters, vol. 9, pp. 215-223, 1987.
11. T. Kobayashi, "Adaptive regulator design of a viscous Burgers' system by boundary control," IMA Journal of Mathematical Control and Information, vol. 18, pp. 427-437, 2001.
12. T. Kobayashi, "Stabilization of infinite-dimensional second-order systems by adaptive PI-controllers," Math. Meth. Appl. Sci., vol. 24, pp. 513-527, 2001.
13. T. Kobayashi, "Adaptive stabilization of the Kuramoto-Sivashinsky equation," Int. J. Systems Science, vol. 33, pp. 175-180, 2002.
14. T. Kobayashi, "Low-gain adaptive stabilization of infinite-dimensional second-order systems," Journal of Mathematical Analysis and Applications, vol. 275, pp. 835-849, 2002.
15. T. Kobayashi, "Adaptive stabilization of infinite-dimensional semilinear second-order systems," IMA Journal of Mathematical Control and Information, vol. 20, pp. 137-152, 2003.
16. M. Krstic, "Lyapunov adaptive stabilization of parabolic PDEs - Part II: Output feedback and other benchmark problems," submitted to 2005 Conference on Decision and Control.
17. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.
18. W. Liu, "Boundary feedback stabilization of an unstable heat equation," SIAM J. Contr. Optim., vol. 42, pp. 1033-1043, 2003.
19. W. Liu and M. Krstic, "Adaptive control of Burgers' equation with unknown viscosity," Int. J. Adapt. Contr. Sig. Proc., vol. 15, pp. 745-766, 2001.
20. H. Logemann and B. Martensson, "Adaptive stabilization of infinite-dimensional systems," IEEE Trans. AC, vol. 37, pp. 1869-1883, 1992.
21. H. Logemann and E. P. Ryan, "Time-varying and adaptive integral control of infinite-dimensional regular linear systems with input nonlinearities," SIAM J. Contr. Optim., vol. 38, pp. 1120-1144, 2000.
22. H. Logemann and S. Townley, "Adaptive stabilization without identification for distributed parameter systems: An overview," IMA J. Math. Control and Information, vol. 14, pp. 175-206, 1997.
23. Y. Orlov, "Sliding mode observer-based synthesis of state derivative-free model reference adaptive control of distributed parameter systems," J. of Dynamic Syst. Mean. Contr., vol. 122, pp. 726-731, 2000.
24. L. Praly, "Adaptive regulation: Lyapunov design with a growth condition," Int. J. Adapt. Contr. Sig. Proc., vol. 6, pp. 329-351, 1992.
25. A. P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev, Integrals and Series, vol. 2: Special Functions, Gordon and Breach, 1986.
26. A. Smyshlyaev and M. Krstic, "Closed form boundary state feedbacks for a class of ID partial integro-differential equations," IEEE Trans. on Automatic Control, Vol. 49, No. 12, pp. 2185-2202, 2004.
27. A. Smyshlyaev and M. Krstic, "Backstepping observers for a class of parabolic PDEs," Systems and Control Letters, in press.
28. A. Smyshlyaev and M. Krstic, paper in preparation.
29. A. Smyshlyaev and M. Krstic, paper in preparation for CDC'05.
30. V. Solo and B. Bamieh, "Adaptive distributed control of a parabolic system with spatially varying parameters," Proc. 38th IEEE Conf. Decision and Control, pp. 2892-2895, 1999.
31. S. Townley, "Simple adaptive stabilization of output feedback stabilizable distributed parameter systems," Dynamics and Control, vol. 5 pp. 107-123, 1995.
32. J. T.-Y. Wen and M. J. Balas, "Robust adaptive control in Hilbert space," J. Math. Analysis and Appl., vol. 143, pp. 1-26, 1989.