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Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Published online by Cambridge University Press:  07 February 2008

Ilyasse Aksikas ,
Joseph J. Winkin  and
Denis Dochain
Ilyasse Aksikas
Affiliation:
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada; aksikas@ualberta.ca
Joseph J. Winkin
Affiliation:
Department of Mathematics, University of Namur (FUNDP), 8 Rempart de la Vierge, 5000 Namur, Belgium; Joseph.Winkin@fundp.ac.be
Denis Dochain
Affiliation:
CESAME, Université Catholique de Louvain, 4-6 avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium; dochain@csam.ucl.ac.be
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Abstract

The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential equation in the space variable. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed.

Keywords

First-order hyperbolic PDE'sinfinite-dimensional systemsLQ-optimal controlstabilityoptimality
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 897 - 908
Copyright
© EDP Sciences, SMAI, 2008

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