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Stackelberg-Nash exact controllability for linear and semilinear parabolic equations

 

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Author: Dias Araruna, Fágner
Fernández Cara, Enrique
Cardoso Santos, Mauricio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 21, 835-856.
Document type: Article
Abstract: This paper deals with the application of Stackelberg–Nash strategies to the control of parabolic equations. We assume that we can act on the system through a hierarchy of controls. A first control (the leader) is assumed to choose the policy. Then, a Nash equilibrium pair (corresponding to a noncooperative multiple-objective optimization strategy) is found; this governs the action of the other controls (the followers). The main novelty in this paper is that, this way, we can obtain the exact controllability to a prescribed (but arbitrary) trajectory. We study linear and semilinear problems and, also, problems with pointwise constraints on the followers.
Cite: Dias Araruna, F., Fernández Cara, E. y Cardoso Santos, M. (2015). Stackelberg–Nash exact controllability for linear and semilinear parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis, 21, 835-856.
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URI: http://hdl.handle.net/11441/42923

DOI: http://dx.doi.org/10.1051/cocv/2014052

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