Stackelberg strategy on a degenerate parabolic equation with missing data

TL;DR

This paper develops a hierarchical control strategy for a degenerate parabolic equation with missing initial data, introducing a new Carleman inequality to establish observability and control results.

Contribution

It introduces a novel Carleman inequality for degenerate systems and combines null controllability with low-regret control in a hierarchical framework.

Findings

Established observability inequality for the degenerate system

Designed a Stackelberg control strategy with hierarchic controls

Proved controllability despite missing initial data

Abstract

This paper deals with the hierarchic control of a degenerate parabolic equation with missing initial condition. We present a Stackelberg strategy combining the concept of null controllability with low-regret control. We assume that we can act on the system through a set of hierarchic controls. The main control called the leader is in charge of the null controllability while the second control named the follower solves an optimal control problem involving a missing data. The main novelty of this work is the derivation of a new Carleman inequality for a degenerate system, which is used in a standard way to show observability inequality of the adjoint degenerate systems.