Controle hierárquico via estratégia de Stackelberg-Nash para controlabilidade de sistemas parabólicos e hiperbólicos

• Autor(a) principal: Silva, Luciano Cipriano da
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9839
• topic: Controlabilidade; Controle hierárquico; Estratégia de Stackelberg-Nash; Desigualdade de observabilidade; Equação do calor; Equação de Burgers; Stackelberg-Nash strategy; Observability inequality; Carleman inequality; Heat equation; Wave equation; Burgers' equation; Controllability; Hierarchic control; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this thesis we presents results on the exact controllability of the partial Di erential Equations (PDEs) of the parabolic and hyperbolic type, in the context of hierarchic control, using the Stackelberg-Nash strategy. In every problems we consider a main control (leader) and two secondary controls (followers). To each leader we obtain a correnponding Nash equilibrium, associated to a bi-objective optimal control problem; then we look for a leader of minimal cost that solves the exact controllability problem. For the parabolic problems we have distributed and boundary controls, now in the hyperbolics every controls are distributed. We consider linear and semilinear cases, which we solve using observability inequality obtained combining right Carleman inequalities. Also we use a xed point method.