Stability Analysis for an Online Evolving Neuro-Fuzzy Recurrent Network

In this chapter, an online evolving neuro-fuzzy recurrent network (ENFRN) is proposed. The network is capable of perceiving the change in the actual system and adapting (self-organizing) itself to the new situation. Both structure and parameters learning take place at the same time. The network generates a new hidden neuron if the smallest distance between the new data and all the existing hidden neurons (the winner neuron) is more than a predefined radius. A new pruning algorithm based on the population density is proposed. Population density is the number of times each hidden neuron is used. If the value of the smallest density (the looser neuron) is smaller than a prespecified threshold, this neuron is pruned. It is proposed to use a modified leastsquares algorithm to train the parameters of the network. The major contributions of this chapter are: (1) The stability of the algorithm of the proposed evolving neuro-fuzzy recurrent network was proven; and (2) the bound of the average identification error was found. Three examples are provided to illustrate the effectiveness of the suggested algorithm based on simulations.