Investigation And Application Of Variable-parameter Noise-tolerant Recurrent Neural Network

As a kind of recurrent neural network,the zeroing neural dynamics(zeroing neural network)model has many applications in the fields of mathematics and engineering due to its parallel distribution characteristics and adaptive ability.In order to quickly and accurately solve time-varying linear equations,time-varying Lyapunov equation and other time-varying problems that frequently occur in engineering and practical problems,this paper studies and presents a series of novel variable-parameter noise-tolerant recurrent neural networks on the basis of the traditional ZNN model.The stability,convergence and robustness of the proposed models are theoretically analyzed.Corresponding numerical and applied experimental results verify the effectiveness and superiority of the proposed variable-parameter noise-tolerant recurrent neural network models.To expand,this paper mainly carried out the following research work.1)A PPZNN,which can achieve fast finite-time convergence,is studied to solve time-varying linear equations.Different from the traditional ZNN,the activation function of PPZNN uses the SBP function,which can achieve finite-time convergence.The design parameters use segmented time-varying parameters.Under the acceleration of the twostage time-varying parameters,the convergence speed of the PPZNN model is much faster than that of the fixed parameters ZNN model with finite time convergence.Moreover,it is proved that the convergence time is shorter at the theoretical level.The simulation results also further show that the proposed PPZNN model has better convergence performance than the original ZNN and its variants.2)An improved predefined convergent NSVPZNN is proposed to solve the timevarying Sylvester equation.Different from previous models,in the NSVPZNN model,a new predefined activation function and specially constructed time-varying parameters are designed and proposed.A novel predefined activation function is designed to reduce the conservativeness of the upper bound on the calculated convergence time.In addition,the upper bound of the convergence time of the NSVPZNN model is theoretically calculated,and the relevant proof of the noise-tolerant performance of the model is also given.Numerical experiments verify that the NSVPZNN model has better performance in solving the Sylvester equation than ZNN,finite-time convergence ZNN,predefined-time convergence ZNN,and other variable-parameter ZNN models.3)Different from the traditional ZNN model and the traditional VPZNN model,a time-varying decay parameter is also investigated on the basis of the predefined convergence function.And in order to solve the dynamic complex-valued Lyapunov equation,a CVPZNN model is established.Different from the traditional ZNN,the CVPZNN has an improved predefined time convergence activation function and two exponentially decaying time-varying parameters,which are utilized to accelerate the convergence speed of the model and enhance the robustness of the model.Also different from the ordinary variable parameter ZNN,the two exponentially decaying time-varying parameters can ensure that the time-varying parameters reach a stable state within a certain period of time.Furthermore,in addition to stability,the predefined time convergence and robustness of the CVPZNN model are also demonstrated theoretically.Numerical simulations verify that the CVPZNN model has better predefined time convergence and robustness in solving dynamic complex-valued Lyapunov equations compared to other models.4)The last work is to apply the design method of the NSVPZNN model to the wheeled manipulator to track the butterfly trajectory and the design method of CVPZNN model to AOA dynamic positioning.In the process of manipulator trajectory tracking in cosine noise environment,the convergence speed and accuracy of the proposed NSVPZNN model are better than the FTZNN model,which further shows the feasibility and effectiveness of the model.In addition,in the process of dynamic positioning,two target trajectories(circular trajectory and four-leaf clover trajectory)are given to test the positioning effect of the models.The results show that under the interference of Gaussian noise,the effect of positioning model designed by CVPZNN model is better than CNFZNN model and traditional pseudo inverse method.