Hierarchic control for a coupled parabolic system

Abstract

In this paper we study a Stackelberg–Nash strategy to control systems of coupled linear parabolic partial differential equations. We assume that we can act on the system through several controls called followers , intended to solve a Nash multi-objective equilibrium, and a single leader control satisfying a null controllability objective. We obtain the existence and uniqueness of the Nash equilibrium, its characterization and the optimal leader control satisfying the null controllability problem.