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

Ilyasse Aksikas; Joseph J. Winkin; Denis Dochain

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 897-908
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Aksikas, Ilyasse, Winkin, Joseph J., and Dochain, Denis. "Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 897-908. <http://eudml.org/doc/250316>.

@article{Aksikas2008,
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. },
author = {Aksikas, Ilyasse, Winkin, Joseph J., Dochain, Denis},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {First-order hyperbolic PDE's; infinite-dimensional systems; LQ-optimal control; stability; optimality; first-order hyperbolic PDE's},
language = {eng},
month = {2},
number = {4},
pages = {897-908},
publisher = {EDP Sciences},
title = {Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems},
url = {http://eudml.org/doc/250316},
volume = {14},
year = {2008},
}

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
DA - 2008/2//
PB - EDP Sciences
VL - 14
IS - 4
SP - 897
EP - 908
AB - 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.
LA - eng
KW - First-order hyperbolic PDE's; infinite-dimensional systems; LQ-optimal control; stability; optimality; first-order hyperbolic PDE's
UR - http://eudml.org/doc/250316
ER -

References

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