Finite-parameter feedback stabilization of original Burgers' equations and Burgers' equation with nonlocal nonlinearities

TL;DR

This paper presents a method for globally stabilizing Burgers' equations, including nonlocal nonlinear variants, using controllers with finitely many parameters, ensuring solutions converge exponentially to desired states.

Contribution

It introduces a finite-parameter feedback control approach for stabilizing Burgers' equations, including nonlocal nonlinearities, with proven exponential convergence.

Findings

Solutions are exponentially stabilized to desired states.

Controllers with finitely many parameters are effective.

The method applies to both original and nonlocal Burgers' equations.

Abstract

We study the problem of global exponential stabilization of original Burgers' equations and the Burgers' equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the controlled equations are steering a concrete solution of the non-controlled system as $t\rightarrow \infty$ with an exponential rate.