Propriedades das funções de base radiais aplicadas à identificação de sistemas dinâmicos não-lineares

Abstract

The work presents an investigation on the monlinear dynamics modelling-relevant properties of the radial basis function mode representation. This enables the development of mechanisms to incorporate auxiliary information regarding the underlving system in the identification process. Models obtained from this grev-box approach are in general more robust aud globallv valid. with low-dimensional parameter spaces and better performance describing the behavior observed in the real system. Along with the main objective a case study of the use of augmented basis functions in RBF models terms. such as a better capacity to perfom well even with a (extrmely) short data set and a more global steady-state behavior. The use of augmented basis functions contributed for the study of how static nonlinearities(stationarys states and eigenvalue function) are mapped in RBF modells. Mathematical expressions showing such nonlinearities as a function of the coefficients of the RBF terms were used to derive structure and parameter constraints that mathematically imposes known fixed points of the underlyng system. Moreover, a simple structure constraint that guarantees constant eigenvalues was proposed. The aplication of the RBF representation in grey-box modelling problems was illustrated by means of some experimental and simulated data.