Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions

TL;DR

This paper establishes null controllability for the anisotropic heat equation with dynamic boundary conditions using a hierarchical Stackelberg-Nash control strategy, employing new Carleman estimates to handle the complex boundary dynamics.

Contribution

It introduces a novel approach combining Stackelberg-Nash strategy with new Carleman estimates for heat equations with dynamic boundary conditions.

Findings

Null controllability achieved for the heat equation with dynamic boundary conditions.

Development of new Carleman estimates tailored for hierarchical control problems.

Effective hierarchical control strategy with one leader and two followers.

Abstract

This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.