Controlabilidade de sistemas de controle lineares

• Ano de defesa: 2015
• Autor(a) principal: João Augusto Navarro Cossich
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Brasil; Departamento de Matemática; Programa de Pós-Graduação em Matemática; UEM; Maringá, PR; Centro de Ciências Exatas
• Palavras-chave em Português: Sistemas de controle; Conjuntos controláveis; Controlabilidade; Grupos de Lie; Semigrupos; Control systems; Control sets; Lie groups; Semigroups; Controllability; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5469

In this work, we studied the general results about control systems on a smooth manifold M , that is, a family of differential equations x?(x) = X(x(t), u(t)) on M , where u : R ? U ? Rm belongs to a function set U which we impose some weak regularities, X : M × Rm ? TM is a C1 map such that for each u ? U , the function Xu : M × TM is a vector field on M. After that we present the control set notion, which is really important to study the controllability of general control sistems, in particular the non linear cases. Finally, we show the main results about the controllability of linear control systems on Rd, which are a particular and very interesting class of control systems. The map X is given by X(x, u) = Ax + Bu, where A ? Rd×d and B ? Rd×m