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

Aksikas, Ilyasse;Winkin, Joseph;Dochain, Denis
(2008) Esaim-control Optimisation And Calculus Of Variations — Vol. 14, n° 4, p. 897-908 (2008)

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Authors
  • Aksikas, Ilyasse
    Author
  • Winkin, JosephUnamur
    Author
  • Dochain, DenisUCLouvain
    Author
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 in finite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium pro. le 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.
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Aksikas, I., Winkin, J., & Dochain, D. (2008). Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems. Esaim-control Optimisation And Calculus Of Variations, 14(4), 897-908. https://doi.org/10.1051/cocv:2008015 (Original work published 2008)