Integração numérica de sistemas não lineares semi-implícitos via teoria de controle geométrico / Numerical integration of non-linear semi-implicit square systems via geometric control theory.

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

04/11/2011

RESUMO

This work improves a method to approximate solutions for a class of differential algebraic equations (DAEs), known as systems semi-implicit square. The method, called here MII, is based on geometric theory of decoupling for nonlinear systems combined with efficient techniques numerical analysis. It uses an algorithum that mixes symbolic and numerical calculations to build an explicit system, whose solutions converge exponentially to solutions of the original implicit system. Two versions of the method are given. The first one is called MIIcond, trying to obtain numerically stable matrices through balancing. The second one is the MIIproj, taking advantage of a geometricinterpretation of the vector field there obtained. The implementations were developed in Matlab/Simulink with the symbolic toolbox. Through benchmarks, including performing comparisons with other methods currently available, it was found that the MIIcond was not feasible in some cases, due to processing time too long. On the other hand, the MIIproj presented itself as good alternative to this class of problems, especially for systems of high index.

ASSUNTO(S)

daes daes geometric control theory integração numérica. numerical integration. semi-implicit square systems sistemas semi-implícitos quadrados teoria de controle geométrico

ACESSO AO ARTIGO

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