TY - JOUR
T1 - Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds
AU - Christofides, Panagiotis D.
AU - Daoutidis, Prodromos
PY - 1997/12/1
Y1 - 1997/12/1
N2 - This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output feedback controllers for systems of quasi-linear parabolic partial differential equations (PDEs), for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast one. Combination of Galerkin's method with a novel procedure for the construction of approximate inertial manifolds for the PDE system is employed for the derivation of ordinary differential equation (ODE) systems (whose dimension is equal to the number of slow modes) that yield solutions which are close, upto a desired accuracy, to the ones of the PDE system, for almost all times. These ODE systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed-loop system to follow up to a desired accuracy, a prespecified response for almost all times.
AB - This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output feedback controllers for systems of quasi-linear parabolic partial differential equations (PDEs), for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast one. Combination of Galerkin's method with a novel procedure for the construction of approximate inertial manifolds for the PDE system is employed for the derivation of ordinary differential equation (ODE) systems (whose dimension is equal to the number of slow modes) that yield solutions which are close, upto a desired accuracy, to the ones of the PDE system, for almost all times. These ODE systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed-loop system to follow up to a desired accuracy, a prespecified response for almost all times.
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M3 - Conference article
AN - SCOPUS:0031389084
VL - 2
SP - 1068
EP - 1073
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
T2 - Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5)
Y2 - 10 December 1997 through 12 December 1997
ER -