Robust Stackelberg controllability for a parabolic equation

TL;DR

This paper develops a novel Stackelberg control strategy for parabolic equations, integrating robustness to disturbances, and introduces a leader-follower framework with a saddle point approach for enhanced controllability.

Contribution

It introduces a new combination of robustness and Stackelberg strategies for controlling parabolic equations, with a saddle point formulation for the follower control.

Findings

Established null controllability with a leader control.

Designed a robust follower control insensitive to disturbances.

Proved existence of saddle points in the control problem.

Abstract

The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability property; additionally, we have a control \textit{the follower} that solves a robust control objective. That means, that we seek for a saddle point of a cost functional. In this way, the follower control is not sensitive to a broad class of external disturbances. As far as we know, the idea of combining robustness with a Stackelberg strategy is new in literature