Metodologia para modelagem de filtros de Kalman nebulosos evolutivos de realização mínima no espaço de estados via dados experimentais

Abstract

This thesis presents a methodology to evolving fuzzy Kalman filter identification. The mathematical formulation adopted contemplates the following aspects: an offline GustafsonKessel (GK) clustering algorithm is applied to input and output experimental data set of dynamic system for rules antecedent parameters initial estimation. Similarly, this algorithm is used to formulate an offline fuzzy version of the Observer/Kalman Filter Identification (OKID) algorithm for rules consequent parameters initial estimation. Since the fuzzy Kalman filter model is obtained from offline way, it will serve as the initial condition for evolving fuzzy Kalman filter online identification. Then, each new sample of input-output experimental data of dynamical system, the eTS (evolving Takagi-Sugeno) evolving clustering algorithm is used to estimate the antecedent parameters to increase, decrease or maintain the same number of rules of the evolving fuzzy Kalman filter obtained in the immediately before sample. An evolving fuzzy version of OKID algorithm, based on eTS evolving clustering is used to estimate the consequent of evolving fuzzy Kalman filter, composed by state matrix, input influence matrix, output influence matrix, direct transmission matrix, and Kalman gain matrix, adapting to the dynamic system behavior represented by each new sample analyzed. Computational results, which are compared to results obtained by other relevant methodologies and widely cited in the literature, present two application examples: the tracking of a non-linear SISO (Single Input, Single Output) system output and the estimation of parameters and states of a system with censored data. Experimental results present two practical applications, such as: trajectory tracking of a Fogtrein-I model rocket or FTI (Foguete de Treinamento – Intermediário, in Portuguese), applied in tests, qualification and training at the Alcântara - Maranhão Launch Center (CLA, Centro de Lançamento de Alcântara, in Portuguese) and the Barreira do Inferno - Rio Grande do Norte Launch Center (CLBI); and the tracking of outputs from helicopter with two degrees of freedom (2DoF Helicopter - Quanser).