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

## TL;DR

This paper demonstrates exponential stabilization of complex Ginzburg-Landau equations using finite-parameter feedback control, which employs a limited number of measurements or modes to control and steer solutions effectively.

## Contribution

It introduces a novel finite-parameter feedback control method for stabilizing and steering solutions of the complex Ginzburg-Landau equation, including a control scheme based on measurements of the uncontrolled system.

## Key findings

- Proves exponential stabilization using finitely many controllers.
- Develops a feedback control to steer solutions to desired states.
- Validates the control approach for complex Ginzburg-Landau equations.

## 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.