Controle Hierárquico da Equação da Onda

Abstract

The present work has the distributed control v applied to the linear wave's equation. We seek to reach two objective, one of the kind Controllability and another the not system state distance to a state y2 (x; t) predefined. This is an problem of multicriteria optimization, and to solves him, introduce the notion Stackelberg's Optimal Control (classical in economy), in which we divide v into two, tell v1 and v2, and each one will act in the respective part from the Boundary 1;2 with a hierarchy between the same. This way, we take over that v1 is the control leader and v1 will be the follower. To leave of this terminogy, we use the idea of the hierarchical control, that is, admit that given a right v1, optimize the second goal concerning v2 and find a relation such that v2 = F (v1). So, the first goal became function of v1, belonging to the kind approximate controlability that will be proved through a density criterion and a Holmgren's uniqueness theorem. Finally, proved for controlability close, from unicidade of the solution, find Optimality system for the control leader.