Modeling of nonlinear systems based on orthogonal neural network with matrix value decomposition

In this paper, a single-layer orthogonal neural network (ONN) which is developed based on orthogonal functions is introduced. Since the processing elements are orthogonal to one another and there is no local minimum of error function, the orthogonal neural network is able to avoid the above problems. Legendred orthogonal polynomial functions are selected as the basic functions of the orthogonal function neural network. Kalman filtering algorithm with singular value decomposition is used to confirm the parameters and weights of the orthogonal function neural network in order to avoid error delivery and error accumulation. To demonstrate the performance of this modeling method, the simulation on Mackey-Glass chaotic time series is performed. The results show that this method provides effective and accurate prediction.