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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.
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Víctor Hernández-Santamaría, Luz de Teresa, Alexander Poznyak, Hierarchic control for a coupled parabolic system. Port. Math. 73 (2016), no. 2, pp. 115–137DOI 10.4171/PM/1979