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.

在本文中，我们提出并研究了一种新型的径向基函数（RBF）神经网络机制，该机制利用凸余弦（RC）函数识别非线性动力系统。在本设计中，RBF神经网络机制利用RC函数代替高斯函数，即RCRBF。安N维RC函数具有常数插值特性，这对于神经网络中的函数逼近误差分析很有帮助。基于多变量RC函数逼近理论，我们研究了如何选择更新的参数以及晶格点中相邻节点的距离。因此，提出的网络可以统一逼近非线性动力学函数。由于持久性激励（PE）在神经网络学习系统中起着重要的作用，因此通过RC函数分析来确定PE条件在输入序列中的行为。权重更新和误差收敛通过Lyapunov函数分析得出结论。为了说明所提出的RCRBF方法的有效性，与GRBF机制相比，以Van Der Pol和Rossler动力学系统为测试示例。