Null controllability and Stackelberg–Nash strategy for a $2\times 2$ system of parabolic equations

Abstract

This paper is dedicated to solving a multi-objective control problem for a $2\times 2$ system of parabolic equations. Here, we have many objectives, possibly conflictive, and we adopt a concept of hierarchy for the controls. We have the leader control, responsible for objectives of controllability type, and the follower controls which intend to be a Nash-equilibrium with respect to some given cost functionals. The novelty here is that we formulate this problem for systems of parabolic equations, meaning that we have many variables and naturally much more objectives to accomplish.