Finite-parameter feedback control for stabilizing the complex Ginzburg–Landau equation

Abstract

In this paper, we prove the exponential stabilization of solutions for complex Ginzburg–Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg–Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.