A neurofuzzy network structure for modelling and state estimation of unknown nonlinear systems

A fuzzy logic system has been shown capable of arbitrarily approximating any nonlinear function, and has been successfully applied to system modelling. The functional rule fuzzy system enables the input-output relation of the fuzzy logic system to be analysed. B-spline basis functions have many desirable numerical properties and as such can be used as membership functions of fuzzy system. This paper analyses the input-output relation of a fuzzy system with a functional rule base and B-spline basis functions as membership functions, constructing a neurofuzzy network for systems representation in which the training algorithm is very simple since the network is linear in the weights. rt is also desired to merge the neural network identification technique and the Kalman filter to achieve optimal adaptive filtering and prediction for unknown but observable nonlinear processes. In this paper the derived neurofuzzy network is applied to state estimation in which the system model identified is converted to its equivalent state-space representation with which a Kalman filter is applied to perform state estimation. Two approaches that combine the neurofuzzy modelling and the Kalman filter algorithm, the indirect method and direct method, are presented. A simulated example is also given to illustrate the approaches based on real data.