Identification of Discrete-Time Dynamical Systems Via Recurrent Fuzzy Models

In recent years, recurrent neural network models have found extensive applications in the identification and control of complex dynamical systems. A wide class of dynamic learning algorithms have been applied to train such models. The objective of this work is to apply concepts and techniques developed in the neural network arena to the fuzzy neural network field. A recurrent fuzzy neural network model is proposed that is called the dynamical-adaptive fuzzy neural network (D-AFNN), which is employed to identify dynamic nonlinear plants. Thefuzzy model is based upon the Takagi-Sugeno inference method with polynomial consequent functions. Training of the recurrent models is performed by means of the epochwise backpropagation through time (BPTT) scheme and the on-line BPTT. The mathematical background of the learning algorithms is presented and the computational procedure providing the error gradients is thoroughly discussed. We present also the rule base adaptation mechanism performing the fuzzy system structure learning. The rule base is constructed via training and a membership insertion mechanism. Simulation results are employed to illustrate the effectiveness of the proposed methodology.