Research On Neural Network Model Of Variable Activation Function Based On Neural Dynamics And Its Application

Time-Varying Linear Equations and Inequalities(LEIS)problems are playing an increasingly prominent role in many scientific and industrial fields,such as optimization problems,motion trajectory problems of robotic arms,and soon.However,at present,we are in the era of big data with high-dimensional data,and it is difficult for algorithms to solve LEIS problems in real-time.Neural dynamics method is a mainstream optimization method,which constructs nonlinear dynamic models based on neural networks for problem solving.In this paper,by introducing non negative relaxation variables,time-varying linear equations and inequality equations are transformed into mixed nonlinear equations.Therefore,the study of neural network models based on neural dynamics methods to solve LEIS problems is of great significance.This article mainly focuses on the following aspects of solving the LEIS problem:1.A novel finite time convergent neural network model with variable parameters and variable activation functions is proposed based on neural dynamics methods for solving LEIS problems.The model no longer relies on special activation functions to achieve finite time convergence,but rather achieves finite convergence from the model construction itself.The activation function used in this network model is no longer single,and multiple activation functions can be combined.The theoretical analysis proves the global convergence,robustness,and finite time convergence of the network model under different activation functions.Then,simulation experiments were conducted to verify the performance of the model,the impact of different parameters on the model,and the comparison with traditional methods.The experimental results further verify the superiority and robustness of the finite time convergence of the model.2.In order to further optimize the convergence performance of the model for solving the LEIS problem,a new neural network model for activation function optimization was proposed using the combined activation function method.By considering the advantages and disadvantages of each activation function,the activation function is combined into a new type of activation function according to a certain weight,and applied to the above model.For the new model,it is theoretically verified that it has finite time convergence and robustness under different activation function combinations.Then,through simulation experiments,the new model using different combinations of activation functions is simulated and compared.Experimental results show that the proposed model has a better convergence effect.3.A nonnegative relaxation variable is added to the repetitive trajectory motion problem of a robotic arm,which is transformed into a LEIS problem.The two models proposed in this paper are used for experimental simulation.Firstly,through simulation experiments,the joint angle of the robot arm is analyzed and the specific drift situation is given.Then,through experiments,the effectiveness and finite time convergence of the two models proposed in this paper in solving the repetitive trajectory motion of a robotic arm in the case of joint angular drift are verified,and through comparative experiments,the higher convergence accuracy of the two models is verified.