Some remarks on the hierarchic control for coupled parabolic PDEs


Hernández-Santamaría V., de Teresa L. Some remarks on the hierarchic control for coupled parabolic PDEs . SEMA SIMAI Springer Series, Vol. 17 (2018), pp.117-137. DOI: 10.1007/978-3-319-97613-6_7

Abstract: In this paper, we study Stackelberg-Nash strategies to control a system of two coupled parabolic equations. We assume that we act in the system by means of a hierarchy of controls. First, controls in each equation, called leaders, optimize their objective, and then a third control, named the follower, reacts optimally to the leaders’ action.We prove an observability inequality for an extended system, which yields the Stackelberg-Nash optimization. Then, we remove the action of one of the leader’s control. In this way, we control a system of various equations by acting only on the first component.

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