Stabilizability for nonautonomous linear parabolic equations with actuators as distributions

TL;DR

This paper investigates the stabilizability of nonautonomous linear parabolic equations with actuators modeled as distributions, constructing explicit and Riccati feedback controls, and demonstrating their effectiveness through simulations.

Contribution

It introduces a stabilizing feedback control for parabolic equations with distributional actuators and analyzes the associated Riccati feedback, expanding control methods for such systems.

Findings

Explicit stabilizing feedback control is constructed.

Riccati feedback control is analyzed for optimal stabilization.

Simulations confirm the effectiveness of both control strategies.

Abstract

The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial domain of concrete parabolic equations. A stabilizing feedback control operator is constructed and given in explicit form. Then, an associated optimal control is considered and the corresponding Riccati feedback is investigated. Results of simulations are presented showing the stabilizing performance of both explicit and Riccati feedbacks.