基于递归神经元网络的动态系统逼近研究

Approximation of Dynamic System by Recurrent Neural Network

目的研究局部递归神经网络的逼近能力，为递归网络在非线性系统辨识和控制中的应用提供理论依据．方法构造一种结构简洁的局部递归网络模型，使用神经网络基本逼近定理、函数分析理论分析它在一定条件下的逼近能力．结果证明了在适当的初始条件下，通过权值训练可使递归网络输出逼近ｎ维动态系统的有限时间轨迹．结论在适当的初始条件下，局部递归网络具有逼近非线性动态系统有限时间响应的能力，数字仿真验证了理论结果的正确性．

Aim\ To study the approximating capacity of a new locally recurrent neural network, and draw much more general conclusions about the nonautonomous system approximation Methods\ A new locally recurrent neural network model was explored, the approximation results were drawn by using the basic neural approximating theorem and other mathematics analyzing theory Results\ Simulation results showed the approximation results were correct and the recurrent neural network was powerful for the nonlinear dynamic system approximation Conclusion\ It is proved that the finite time trajectories of a given n dimensional nonlinear dynamic system with a control input can be approximatd by the states of the locally recurrent network under the condition of the same input and approximate initial states