Adaptive Fuzzy Neural Networks as identifiers of discrete-time nonlinear dynamic systems

An adaptive supervised learning scheme is proposed in this paper for training Fuzzy Neural Networks (FNN) to identify discrete-time nonlinear dynamical systems. The FNN constructs are neural-network-based connectionist models consisting of several layers that are used to implement the functions of a fuzzy logic system. The fuzzy rule base considered here consists of Takagi-Sugeno IF-THEN rules, where the rule outputs are realized as linear polynomials of the input components. The FNN connectionist model is functionally partitioned into three separate parts, namely, the premise part, which provides the truth values of the rule preconditional statements, the consequent part providing the rule outputs, and the defuzzification part computing the final output of the FNN construct. The proposed learning scheme is a two-stage training algorithm that performs both structure and parameter learning, simultaneously. First, the structure learning task determines the proper fuzzy input partitions and the respective precondition matching, and is carried out by means of the rule base adaptation mechanism. The rule base adaptation mechanism is a self-organizing procedure which progressively generates the proper fuzzy rule base, during training, according to the operating conditions. Having completed the structure learning stage, the parameter learning is applied using the back-propagation algorithm, with the objective to adjust the premise/consequent parameters of the FNN so that the desired input/output representation is captured to an acceptable degree of accuracy. The structure/parameter training algorithm exhibits good learning and generalization capabilities as demonstrated via a series of simulation studies. Comparisons with conventional multilayer neural networks indicate the effectiveness of the proposed scheme.