Recobrimento monotônico de sistemas de controle / Monotonic covering of control systems
AUTOR(ES)
Rodrigo Ribeiro Lopes
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
27/02/2012
RESUMO
In this work, we deal with monotonic homotopy between trajectories of a control system \ SIIGMA\ on a manifold M. This is an apropriate variant of usual homotopy, where two trajectories are considered to be homotopic if they can be deformed to each other in a continuous way through trajectories. We introduce regularity for controls and consider monotonic homotopy between trajectories generated by regular controls. In particular, we present an example of a system having homotopic trajectories which are not monotonically homotopic. The main goal was to understand the construction for monotonic homotopy of the universal covering space and, in particular, the differentiable manifold structure on the set \ \\GAMA\ (\ SIGMA\ , x) of monotonic homotopy classes of trajectories starting at x M. As a consequence of that result, we obtain a local diffeomorphism which permits lifting of \ SIGMA\ to another system \ SIGMA SUP. E\ in \ \\GAMA\ (\ SIGMA\ , x). To consider universal properties of \ \\GAMA\ (\ SIGMA\ , x) we take a covering : N \ A IND.R\ (\ SIGMA\ , x) in the sense that N is a differentiable manifold provided with a control system \ SIGMA SUP. E\ and is a local diffeomorphism mapping \ SIGMA SUP. DA ORDEM DE\ to \ SIGMA\ . Comparing the trajectories of \ SIGMA SIGMA. E\ and \ SIGMA SUP. DA ORDEM DE\ we construct a lifting mapping f : \ \\GAMA\ (\ SIGMA, x) \ SETA\ N that relates \ SIGMA SUP. E\ e \ SIGMA SUP. DA ORDEM DE\ . Finally, we take into account the particular class of symmetric systems, for which both coverings \ \\GAMA(\ SIGMA, x) and \ M SUP. DA ORDEM DE\ coincide
ASSUNTO(S)
recobrimento universal control systems homotopia monotônica monotonic homotopy sistemas de controle universal covering
