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.
Mots clés : first-order hyperbolic PDE's, infinite-dimensional systems, LQ-optimal control, stability, optimality
@article{COCV_2008__14_4_897_0,
author = {Aksikas, Ilyasse and Winkin, Joseph J. and Dochain, Denis},
title = {Optimal {LQ-feedback} control for a class of first-order hyperbolic distributed parameter systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {897--908},
publisher = {EDP-Sciences},
volume = {14},
number = {4},
year = {2008},
doi = {10.1051/cocv:2008015},
mrnumber = {2455389},
zbl = {1148.49033},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2008015/}
}
TY - JOUR AU - Aksikas, Ilyasse AU - Winkin, Joseph J. AU - Dochain, Denis TI - Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 897 EP - 908 VL - 14 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008015/ DO - 10.1051/cocv:2008015 LA - en ID - COCV_2008__14_4_897_0 ER -
%0 Journal Article %A Aksikas, Ilyasse %A Winkin, Joseph J. %A Dochain, Denis %T Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 897-908 %V 14 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008015/ %R 10.1051/cocv:2008015 %G en %F COCV_2008__14_4_897_0
Aksikas, Ilyasse; Winkin, Joseph J.; Dochain, Denis. Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 897-908. doi : 10.1051/cocv:2008015. http://www.numdam.org/articles/10.1051/cocv:2008015/
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