Identification of Nonlinear Dynamical System Based on Raised-Cosine Radial Basis Function Neural Networks

In this paper, we present and investigate a new type of radial basis function (RBF) neural networks mechanism using raised-cosine (RC) function to identify nonlinear dynamic system. In this design, the RBF neural networks mechanism utilizes RC function to replace Gaussian function, which is called RCRBF. An N-dimensional RC function has the constant interpolation property, which is benefit for the function approximating errors analysis in the neural networks. Based on multivariable RC function approximation theory, we develop how to select the updated parameters and the distance of adjacent nodes in lattice points. Therefore, the proposed networks can uniformly approximate nonlinear dynamical function. As persistency excitation (PE) plays an important part in neural networks learning system, how does PE condition behave in input sequences is formulated by RC function analysis. The weights updating and errors convergence are concluded by Lyapunov function analysis. To illustrate the effectiveness of the proposed RCRBF method, Van Der Pol and Rossler dynamical system are used as test examples, in comparison with GRBF mechanism. The results show that the proposed method has better accurate identification and approximating effect than that of GRBF mechanism.