Volume 14, Number 4, October-December 2008
|Page(s)||897 - 908|
|Published online||07 February 2008|
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada; email@example.com
2 Department of Mathematics, University of Namur (FUNDP), 8 Rempart de la Vierge, 5000 Namur, Belgium; Joseph.Winkin@fundp.ac.be
3 CESAME, Université Catholique de Louvain, 4-6 avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium; firstname.lastname@example.org
Revised: 30 July 2007
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.
Mathematics Subject Classification: 49J20 / 93B52 / 34K30 / 47H06 / 34K20
Key words: First-order hyperbolic PDE's / infinite-dimensional systems / LQ-optimal control / stability / optimality
© EDP Sciences, SMAI, 2008
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