Application Of Modified Recurrent Neural Network Design Against Noise

Scientific computing problems(i.e.matrix pseudoinverse and quadratic programming)widely exist in science,industry and other fields.but such mathematical problems usually involve time-varying factors,so the corresponding mathematical problems also have time-varying characteristics.However,traditional methods(i.e.Newton’s method and Gradient Neural Network)are not suitable for solving time-varying problems.Since the Zeroing neural network(ZNN)was proposed,it has been widely used to solve various time-varying problems.Both theoretical and numerical results show that ZNN model can accurately and effectively solve time-varying problems.It is worth noting that noise substantially influences the accuracy of neural networks models in the process of solving the problems.Nevertheless,the existing neural network models show limited capacity of noise tolerance,which may seriously affect their application in practical problems.Therefore,in order to solve real-time scientific calculation problems quickly,noises must be taken into account in order to achieve higher calculation accuracy.In particular,most of the current studies are aimed at constant noise,linear noise and other types of noise.There is a lack of adaptive mechanism for harmonic noise rejection,which seriously affects the calculation accuracy of ZNN model.Aiming at the above problems,this paper mainly has the following research results:1.Aiming at the problem that the noise tolerance ability of neural network model in solving time-dependent quadratic programming is limited,considering the influence of activation function on the convergence speed of neural network model,two nonlinear activation functions are designed to make the ZNN model converge in predefined-time and improve the noise tolerance ability,a prescribed-time convergent and noise-tolerant zeroing neural network(PTCNTZNN)model is proposed to calculate the time-dependent quadratic programming problem in noise environment.Theoretical analyses of the PTCNTZNN model show that it can be accelerated to prescribed-time convergence to the time-dependent optimal solution,and has natural anti-noise ability.The upper bound of the convergence time is also derived theoretically.Finally,the performance of the PTCNTZNN model was verified by experiments,and the results substantiate the excellent robustness and convergence characteristics of the proposed PTCNTZNN model for calculating real-time-dependent quadratic programming problem as compared with the existing ZNN models.2.In view of the influence of harmonic noise on the solution accuracy of ZNN model,a novel harmonic noise-tolerant ZNN model with fast convergence rate are first proposed and investigated for computing dynamic matrix pseudoinversion by combining the dynamic properties of harmonic signals and the Li activation function.From a theoretical perspective,such ZNN model,which incorporates the dynamics of harmonic signal,can enforce the convergence of the residual error to zero in noisy environments.Subsequently,the extended ZNN model with robustness against multiple-harmonic noise was developed.As a case study,the proposed ZNN models were verified for solving the problem of dynamic matrix pseudoinversion in the presence of harmonic noise.The experiment results are illustrated,which further substantiate the efficacy and superiority of the proposed HNTZNN models for the dynamic matrix pseudoinversion under low-frequency,high-frequency,periodic and aperiodic harmonic noises.3.The proposed HNTZNN models are applied to the kinematic control of a four-link planar robot manipulator in the presence of harmonic noise.Through the pseudoinverse-type(P-type)scheme of the manipulator,a ZNN-combined kinematic control method that is tolerant to single-harmonic noise and a ZNN-combined kinematic control method for multiple-harmonic noise are desiged.Tricuspid path-tracking and circular path-tracking examples prove that the presented ZNN-combined kinematic control methods are more effective for the robot manipulator under the presence of harmonic noise.Thereby depicting the application prospect of the proposed HNTZNN models.