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Numerical approximation of the LQR problem in a strongly damped wave equation

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Abstract

The aim of this work is to obtain optimal-order error estimates for the LQR (Linear-quadratic regulator) problem in a strongly damped 1-D wave equation. We consider a finite element discretization of the system dynamics and a control law constant in the spatial dimension, which is studied in both point and distributed case. To solve the LQR problem, we seek a feedback control which depends on the solution of an algebraic Riccati equation. Optimal error estimates are proved in the framework of the approximation theory for control of infinite-dimensional systems. Finally, numerical results are presented to illustrate that the optimal rates of convergence are achieved.

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Correspondence to Dante Kalise.

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Hernández, E., Kalise, D. & Otárola, E. Numerical approximation of the LQR problem in a strongly damped wave equation. Comput Optim Appl 47, 161–178 (2010). https://doi.org/10.1007/s10589-008-9213-6

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  • DOI: https://doi.org/10.1007/s10589-008-9213-6

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