Recurrent Neural Network Approach With Its Applications On Nonlinear System Tracking-control

The network structure of recursive neural network consists of one or more feedback loops,which can realize the real modeling for nonlinear system. It may exist such as poor network approximation performance and stability convergence performance because of the complex network structure characteristics. Recursive neural network generally contains dynamic recurrent neural network and static recursive neural network. In this paper, according to Zhang et al’s design idea, we study, investigate and develop a novel recursive neural network method(NRNN). The network algorithm could make full use of the information of time derivative for coefficient, which is usually applied to time-varying problems solving frequently encountered in practical engineering.In general, traditional recursive neural network based on gradient method(GNN) is often defined a non-negative energy function based on the scalar norm value, and it can only be used to solve the matrix equation of constant coefficient accurately and effectively. Compared with GNN, NRNN model is expressed in implicit dynamics equation, while dynamic equation of gradient neural network model is dominant.This paper mainly researches on the following questions, and achieves lots of results.1) Study the recursive neural network models for the time-varying coefficient matrix equation model. According the neural dynamics design method of Zhang et al, an error function will be introduced to recurrent neural network during the design procedure. Hence, an unbounded novel recurrent neural network model based on matrix value is developed. Mathematical theory analysis and experimental simulation results show that NRNN can make neural solution approximate to the theoretical solution accurately and keep stable. Compared with traditional gradient algorithm,NRNN could obtain better error convergence performance.2) Study the constant matrix equation solving and the establishment of corresponding SIMULINK model. As a special case of time-varying matrix equation, the steady matrix equation is a relatively special engineering. In this paper, the presented recursive neural network method is applied to time-varying constant matrix analytic and SIMULINK model. Simulation analysis further shows accuracy and effectiveness of the NRNN method for this matrix equation.3) Study the application of the recursive neural network in nonlinear tracking control system.Under the environment of NRNN and GNN feasible, combining effective use of NRNN algorithm with the time derivation of information and GNN algorithm along the negative gradient direction derivative, we put forward a controller design method based on recurrent neural network to tacklethe problem of tracking control for nonlinear system accurately and effectively. The algorithm could effectively avoid the existing singular value problems during the design process.These two kinds of recursive neural network algorithm are verified with validity and accuracy based on the time-varying matrix problem analysis and with constant matrix equation by SIMULINK circuit simulation in this article. Additionally, according to input and output characteristics of strict-feedback nonlinear system, we investigate and design a new kind of design method of nonlinear system control model through making full use of NRNN and GNN algorithm.The method can be used to solve output tracking control problem of strict feedback nonlinear system effectively. The three study cases show the superiority the accuracy of the presented recursive neural network. The design algorithm of nonlinear system control model(N-G) may be regarded as NRNN and GNN comprehensive application to some extent.