Research On Filtering Problems Of Lagrangian Systems

Lagrangian systems are a typical of systematic models with obvious physical implications and broad practical background. Analysis of many complicated controlled objects in engineering and studies on some theoretical problems can be transmitted into researches on Lagrangian systematic models. Typically, Lagrangian systems are a kind of nonlinear systems with state couplings, which is their typical nature. Therefore, the research into filtering problems of Lagrangian systems makes it possible to solve filtering problems of a wide class of non-linear systems, thus providing a paradigm for researches on filtering problems of non-linear systems.The thesis concentrates on solving state filtering estimation problem of Lagrangian systems under disturbance of noise, which is of great value both practically and theoretically. The relevant researches of this thesis are well arranged under the frame of nonlinear filtering theory and random theory. Firstly, the kinetic characteristics of Lagrangian systems are analysed, on witch we bring up with a discretizated model under the principle of conservation of energy. Secondly, we bring up with some necessary assumptions in terms of filtering problems after offering the state-space representation of Lagrangian systems,thus making the model more completed. Moreover, the linearization model and Bayesian probability model are set up for subsequent analysis. Finally, we conducted simulation experiments on four different filtering methods on basis of the model obtained earlier.As for the results, advantages and disadvantages are discussed, thus giving advice to the future development of filtering problems of lagrangian systems.In this thesis, we conducted a research on Lagrangian systems systematically, and bring up with a relatively completed model, hoping to provide a certain paradigm for filtering problems of a typical class of nonlinear systems. All our work is based on the deep analysis of kinetic and probabilistic characteristics. Meanwhile, several different filtering methods applied on Lagrangian systematic models are discussed, with improved schemes given for unstable situations. Therefore, both the model we bring up with and the improvement of the filtering methods can be considered as a paradigm, having potential for both practical and theoretical uses.