The $H^{\infty}$-control problem for parabolic systems with singular Hardy potentials

TL;DR

This paper addresses the $H^{ abla}$-control problem for parabolic systems with Hardy potentials, providing solutions for boundary and distributed control scenarios in infinite-dimensional settings.

Contribution

It introduces a novel approach to the $H^{ abla}$-control problem for parabolic PDEs with singular Hardy potentials, including boundary and distributed control cases.

Findings

Successfully solves the $H^{ abla}$-control problem for systems with Hardy potentials.

Provides explicit control strategies for boundary and distributed controls.

Extends control theory to PDEs with singular potentials.

Abstract

We solve the $H^{\infty}$-control problem with state feedback for infinite dimensional boundary control systems of parabolic type with distributed disturbances and apply the results to equations with Hardy potentials with the singularity inside or on the boundary, in the cases of a distributed control and of a boundary control.