Geodesic
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 897-908

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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.

DOI : 10.1051/cocv:2008015
Classification : 49J20, 93B52, 34K30, 47H06, 34K20
Keywords: first-order hyperbolic PDE's, infinite-dimensional systems, LQ-optimal control, stability, optimality 
@article{COCV_2008__14_4_897_0,
     author = {Aksikas, Ilyasse and Winkin, Joseph J. and Dochain, Denis},
     title = {Optimal {LQ-feedback} control for a class of first-order hyperbolic distributed parameter systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {897--908},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {4},
     year = {2008},
     doi = {10.1051/cocv:2008015},
     mrnumber = {2455389},
     zbl = {1148.49033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008015/}
}
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Aksikas, Ilyasse; Winkin, Joseph J.; Dochain, Denis. Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 897-908. doi: 10.1051/cocv:2008015

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