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Portugaliae Mathematica

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Volume 73, Issue 2, 2016, pp. 115–137
DOI: 10.4171/PM/1979

Published online: 2016-03-24

Hierarchic control for a coupled parabolic system

Víctor Hernández-Santamaría[1], Luz de Teresa[2] and Alexander Poznyak[3]

(1) CINVESTAV del IPN, Mexico, D.F., Mexico
(2) Universidad Nacional Autonoma de México, México, D.F., Mexico
(3) CINVESTAV del IPN, Mexico, D.F., Mexico

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.

Keywords: Controllabilty, Stackelberg–Nash strategies, Carleman inequalities, parabolic systems

Hernández-Santamaría Víctor, de Teresa Luz, Poznyak Alexander: Hierarchic control for a coupled parabolic system. Port. Math. 73 (2016), 115-137. doi: 10.4171/PM/1979