Impulse output rapid stabilization for heat equations

TL;DR

This paper introduces a novel feedback law for heat equations that achieves rapid stabilization using impulse controls active in subdomains at discrete times, based on linking observations, control, and inverse source problems.

Contribution

It presents a new feedback law for heat equations with controls and observations in different subdomains at discrete times, enabling rapid stabilization.

Findings

Achieves rapid stabilization of heat equations.

Develops a feedback law based on impulse control and observation estimates.

Links inverse source problems with control strategies.

Abstract

The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\Omega $ and at discrete time points; Second, The observations are made in another subdomain and at different discrete time points. Our strategy consists in linking an observation estimate at one time, minimal norm impulse control, approximate inverse source problem and rapid output stabilization.