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first-order hyperbolic pde's

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
Ilyasse Aksikas, Joseph J. Winkin, Denis Dochain
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 4 / October 2008

Published online by Cambridge University Press:

07 February 2008, pp. 897-908

Print publication:

October 2008
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The Linear-Quadratic (LQ) optimal control problem is studied for aclass of first-order hyperbolic partial differential equation modelsby using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-spacedescription. First the dynamical properties of the linearized modelaround some equilibrium profile are studied. Next the LQ-feedbackoperator is computed by using the corresponding operator Riccatialgebraic equation whose solution is obtained via a relatedmatrix Riccati differential equation in the space variable. Then thelatter is applied to the nonlinear model, and the resultingclosed-loop system dynamical performances are analyzed.