@article{b4c9c15f6e724c0f84d607fe3c547795,
title = "Analysis and control of parabolic PDE systems with input constraints",
abstract = "This paper develops a general framework for the analysis and control of parabolic partial differential equations (PDE) systems with input constraints. Initially, Galerkin's method is used for the derivation of ordinary differential equation (ODE) system that capture the dominant dynamics of the PDE system. This ODE systems are then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed-loop stability in the presence of constraints. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator. The theoretical results are used to stabilize an unstable steady-state of a diffusion-reaction process using constrained control action.",
author = "El-Farra, {Nael H.} and Antonios Armaou and Christofides, {Panagiotis D.}",
note = "Funding Information: Panagiotis D. Christofides was born in Athens, Greece, in 1970. He received the Diploma in Chemical Engineering degree, in 1992, from the University of Patras, Greece, the M.S. degrees in Electrical Engineering and Mathematics, in 1995 and 1996, respectively, and the Ph.D. degree in Chemical Engineering, in 1996, all from the University of Minnesota. Since July 1996 he has been with the Department of Chemical Engineering at the University of California, Los Angeles, where he is currently Associate Professor. His theoretical research interests include nonlinear control, singular perturbations, and analysis and control of distributed parameter systems, with applications to advanced materials and semiconductor processing, nanotechnology, biosystems, and fluid flows. He has published over 120 refereed articles and two books entitled “Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes” with Birkhauser in 2001 and “Model-Based Control of Particulate Processes” with Kluwer Academic in 2002. A description of his current research projects and a list of his publications can be found at http://www.chemeng.ucla.edu/pchristo/index.html . Professor Christofides has been a member of the Control Systems Society Conference Editorial Board since 2000 and has organized several invited sessions at the Conference on Decision and Control and the American Control Conference. He recently edited a special issue of the Journal Computers and Chemical Engineering on Control of Distributed Parameter Systems which was published in August of 2002. He will be the Program Coordinator of the Applied Mathematics and Numerical Analysis Area of AIChE for 2004, the Program Vice-Chair for Invited Sessions for the 2004 American Control Conference and an Associate Editor of IEEE Transactions on Automatic Control in 2003. Professor Christofides has received the Teaching Award from the AIChE Student Chapter of UCLA in 1997, a Research Initiation Award from the Petroleum Research Fund in 1998, a CAREER award from the National Science Foundation in 1998, the Ted Peterson Student Paper Award from the Computing and Systems Technology Division of AIChE in 1999, the O. Hugo Schuck Best Paper Award from the American Automatic Control Council in 2000, and a Young Investigator Award from the Office of Naval Research in 2001. Funding Information: Financial support, in part by Air Force Office of Scientific Research and The National Science Foundation CTS-9733509 and CTS-0002626, is gratefully acknowledged. ",
year = "2003",
month = apr,
doi = "10.1016/S0005-1098(02)00304-7",
language = "English (US)",
volume = "39",
pages = "715--725",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
number = "4",
}