Szukana fraza: [Abstract = "Then, the Karhunen\-Loéve expansion is directly applied to the ensemble of solutions to derive a small set of empirical eigenfunctions \(dominant spatial patterns\) that capture almost all the energy of the ensemble of solutions. The empirical eigenfunctions are subsequently used as basis functions within a Galerkin model reduction framework to derive loworder ordinary differential equation \(ODE\) systems that accurately describe the dominant dynamics of the PDE system. The ODE systems are subsequently used for the synthesis of nonlinear output feedback controllers using geometric control methods."]

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