Formulações convexas para problemas de controle H2 - robusto relativo a pertubações não-paramétricas

• Autor(a) principal: Freire, Emerson Souza
• Data de Publicação: 2006
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/56
• topic: Controle robusto; Pertubações não-paramétricas; Formulações convexas; Otimização; Robust controller; Non-parametric pertubations; Convex formularizations; Optimization; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::COMPUTABILIDADE E MODELOS DE COMPUTACAO

In this work, performance analysis and control synthesis for good performance are studied for systems subject to non-parametric perturbations which satisfy a prescribed norm bound. First, the performance analysis problem is considered for a given controller that ensures robust stability in presence of such perturbations.. The performance index used is the so-called worst-case index. Due to the the character of the correspondent non-convex problem, convex optimization problems in function spaces are formulated whose solutions are upper bounds on the worst-case index. Next, it is shown that when the decision variables are confined to finite dimensional subspaces, these problems can be formulated in terms of linear optimization problems in euclidean spaces with constraints defined by linear matrix inequalities (LMI s). On the basis of the upper bounds obtained, procedures for controller synthesis can be formulated, which consist of a D-K iteration procedure for minimization problems with respect to multipliers and robust satabilizing controllers. Using the Youla parametrization of these controllers, for a given set of multipliers it is shown that when the Youla parameter is confined to finite dimensional subspace, the synthesis formulations are equivalent to linear optimization problems in euclidean spaces with constraints defined by LMIs. In both the cases (analysis and synthesis) heuristics to iterative modify the confining subspaces are suggested. An approach analogous to the one robust problems was applied to robust filtering problems leading to similar results. It is worth noting that in this case, due to the fact that only open-loop systems are involved, the correspondent synthesis procedures do not require D-K itearation..