Estimação de estados e parâmetros de um pêndulo duplo caótico

Abstract

The analysis of dynamical systems that exhibit chaotic behavior is a subject that has been attracting interests of many researchers. Studies related to system identification and state estimation are important in order to achive a good characterization of the dynamics of such systems on many aspects. Moreover, this kind of studies became challenging, essentially, because there is no such an unified methodology to be applied to the whole class of chaotic systems. In this work, the chaotic double pendulum platform available at the laboratory of Modeling, Analisys and Control of Nonlinear Systems from the Electronics Engineering Department of the Federal University of Minas Gerais is investigated. We aim at applying a nonlinear systems filtering tool, called unscented Kalman filter, to obtain simultaneously state and some parameters estimates for this system simultaneously. Experiments using simulated and experimental data are carried. The filter’s performance is verified for the case of state estimation as well as for the case of joint state-and-parameter estimation. Several conditions concerning the filtering process, such as the type of measured states and measurement sparsity, are tested and the filters strengths and weaknesses are studied for this application.