Finite-dimensional approximation and control of non-linear parabolic PDE systems

International Journal of Control

Volumn 73, Issue 5, 2000, Pages 439-456

  Baker, James ^a   Christofides, Panagiotis D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL VAPOR DEPOSITION; CLOSED LOOP CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK CONTROL; GALERKIN METHODS; LINEAR CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; THIN FILMS;

LINEAR CONTROLLERS;

NONLINEAR SYSTEMS;

EID: 0034689117     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/002071700219614     Document Type: Article

References (28)

1. Banerjee, S., Cole, J.V., and Jensen, K.F., 1998, Nonlinear model reduction of rapid thermal processing systems. IEEE Transactions on Semiconductor Manufacturing, 11, 266-275.
2. Bangia, A.K., Batcho, P.F., Kevrekidis, I.G., and Karniadakis, G.E., 1997, Unsteady 2-D flows in complex geometries: comparative bifurcation studies with global eigenfunction expansion. SIAM Journal on Scientific Computing, 18, 775-805.
3. Balas, M.J., 1979, Feedback control of linear diffusion processes. International Journal of Control, 29, 523-533.
4. Balas, M.J., 1991, Nonlinear finite-dimensional control of a class of nonlinear distributed parameter systems using residual mode filters: a proof of local exponential stability. Journal of Mathematical Analysis and Applications, 162, 63-70.
5. Breedijk, T., Edgar, T.F., and Trachtenberg, I., 1993, A model predictive controller for multivariable temperature control in rapid thermal processing. Proceedings of American Control Conference, San Francisco, CA, USA, pp. 2980-2984.
6. Chen, C.C., and Chang, H.C., 1992, Accelerated disturbance damping of an unknown distributed system by nonlinear feedback. AIChE Journal, 38, 1461-1476.
7. Christofides, P.D., 1998, Robust control of parabolic PDE systems. Chem. Eng. Sci., 53, 2949-2965.
8. Christofides, P.D., 2000, Nonlinear and Robust Control of PDE Systems.' Methods and Applications to Transport-Reaction Processes (Boston: Birkhäuser), to appear.
9. Christofides, P.D., and Daoutidis, P., 1996a, Nonlinear control of diffusion-convection-reaction processes. Comp. Chem. Engng., 20(s), 1071-1076.
10. Christofides, P.D., and Daoutidis, P., 1996b, Feedback control of hyperbolic PDE systems. AIChE Journal, 42, 3063-3086.
11. Christofides, P.D., and Daoutidis, P., 1997, Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds. Journal of Mathematical Analysis and Applications, 216, 398-420.
12. Foias, C., Sell, G.R., and Titi, E.S., 1989, Exponential tracking and approximation of inertial manifolds for dissipative equations. Journal of Dynamics and Differential Equations, 1, 199-244.
13. Fukunaga, K., 1990, Introduction to Statistical Pattern Recognition (New York: Academic Press).
14. Graham, M.D., and Kevrekidis, I.G., 1996, Alternative approaches to the Karhunen-Loéve decomposition for model reduction and rata analysis. Comp. & Chem. Eng., 20, 495-506.
15. Holmes, P., Lumley, J.L., and Berkooz, G. 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, (New York: Cambridge University Press).
16. Isidori, A., 1989, Nonlinear Control Systems: An Introduction (Berlin: Springer-Verlag).
17. Kiether, W.J., Fordham, M.J., Yu, S., Neto, J.S., Conrad, K.A., Hausur, J.R., Sorrell, F.Y., and Wortman, J.J., 1994, Three-zone rapid thermal processor system. Proceedings of 2nd International RTP Conference, pp. 96-101.
18. Khalil, H.K., 1992, Nonlinear Systems (New York: Macmillan Publishing Company).
19. Kokotovic, P.V., Khalil, H.K., and O'Reilly, J., 1986, Singular Perturbations in Control.' Analysis and Design (London: Academic Press).
20. Marquardt, W., 1990, Traveling waves in chemical processes. Int. Chem. Engng., 4, 585-606.
21. Park, H.M., and Cho, D.H., 1996, The use of the Karhunen-Loéve decomposition for the modeling of distributed parameter systems. Chem. Eng. Sci., 51, 81-98.
22. Ray, W.H., 1981, Advanced Process Control (New York: McGraw-Hill).
23. Shvartsman, S.Y., and Kevrekidis, I.G., 1998, Nonlinear model reduction for control of distributed parameter systems: a computer assisted study. AIChE Journal, 44, 1579-1595.
24. Sirovich, L., 1987a, Turbulence and the dynamics of coherent structures: part I: coherent structures. Quarterly of Applied Mathematics, XLV, 561-571.
25. Sirovich, L., 1987b, Turbulence and the dynamics of coherent structures: part II: symmetries and transformations. Quarterly of Applied Mathematics, XLV, 573-582.
26. Temam, R., 1988, Infinite-Dimensional Dynamical Systems in Mechanics and Physics (New York: Springer-Verlag).
27. Theodoropoulou, A., Adomaitis, R.A., and Zafiriou, E., 1998, Model reduction for optimization of rapid thermal chemical vapor deposition systems. IEEE Transactions on Semiconductor Manufacturing, 11, 85-98.
28. Theodoropoulou, A., Adomaitis, R.A., and Zafiriou, E., 1999, Inverse model based real-time control for temperature uniformity of RTCVD. IEEE Transactions on Semiconductor Manufacturing, 12, 87-101.