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We present a computational study of a simple finite-dimensional feedbackcontrol algorithm for stabilizing solutions of infinite-dimensional dissipativeevolution equations such as reaction-diffusion systems, the Navier-Stokesequations and the Kuramoto-Sivashinsky equation. This feedback control schemetakes advantage of the fact that such systems possess finite number ofdetermining parameters or degrees of freedom, namely, finite number ofdetermining Fourier modes, determining nodes, and determining interpolants andprojections. In particular, the feedback control scheme uses finitely many ofsuch observables and controllers that are acting on the coarse spatial scales.We demonstrate our numerical results for the stabilization of the unstable zerosolution of the 1D Chafee-Infante equation and 1D Kuramoto-Sivashinkskyequation. We give rigorous stability analysis for the feedback controlalgorithm and derive sufficient conditions relating the control parameters andmodel parameter values to attune to the control objective.

Finite determining parameters feedback control for distributed nonlinear dissipative systems - a computational study