Hernández-Santamaría V., de Teresa L. Some remarks on the hierarchic control for coupled parabolic PDEs , DOI: To appear
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.