Research On Non-linear And Noise-tolerant Annihilation Neural Network And Its Application In Optimization Calculation

In 2002,the Zeroing neural network(ZNN),a special kind of RNN,was proposed for the time-varying problem.Compared to the gradient neural network(GNN)and other traditional methods,the neural state solution obtained by the ZNN can accurately converge to the theoretical solution.However,in the implementation of RNN,there are always implementation errors that are more complicated than ideal,such as differential errors and model implementation errors that occur with high probability,and errors caused by environmental interference or other external disturbances.Under this background,the neural state solution synthesized by the ZNN will not be accurate,especially for time-varying noise.Therefore,a nonlinear and noise-tolerant ZNN called NNT-ZNN is proposed in this study.The performance of the resultant NNT-ZNN model is analyzed concretely through four applications including the time-varying linear matrix equations solving,the time-varying and static matrices square roots finding,robot consensus and time-varying quadratic minimization problem.The specific work is described as follows:(1)An integration-enhanced matrix-valued error function evolution formula is proposed,which is the basis of synthesizing NNT-ZNN model.Compared with the ZNN,the synthesized NNT-ZNN model greatly reduces the large lagging error left by the ZNN model under noise.Different problems will correspond to different NNT-ZNN models,due to the solved problems are different.(2)Based on the designed evolutionary formula,the NNT-ZNN model corresponding to the time-varying linear matrix equations solving problem is proposed.The convergences of the NNT-ZNN model under both zero noise and noise pollution are theoretically analyzed.MATLAB simulation further validates the correctness of theoretical analyses.Compared with the ZNN,the experimental results better reveal the superiority of the proposed NNT-ZNN model.(3)For the time-varying and static positive definite matrices square roots finding problems,the influence of design parameters on the convergence rate of the related NNT-ZNN model is discussed.At the same time,based on the constant noise and random noise respectively,the convergences of the NNT-ZNN model are also discussed.It is concluded that when the design parameters are increased,the convergence time can be shorted.For both constant and random noise,the NNT-ZNN can still perfectly track the theoretical solution.(4)Based on the all-to-all and limited communication topologies,respectively,the multi-robot consensus problem is investigated.The resultant neural consensus method successfully makes multiple robot nodes located in different locations in the workspace reach the same location.In this approach,the control behavior of the robot node does not depend on the communication topology and a robot only communicates with its own one-hop neighbors.In this study,how to realize specific formations for robots is also discussed.Through a specific transformation,six robot nodes form a hexagonal formation.(5)For the time-varying quadratic minimization problem,this paper constructs the corresponding NNT-ZNN model by zeroing the partial derivatives of the considered problem.The effect of the NNT-ZNN model disturbed by time-varying differential error and dynamic implementation error on the achieved residual error is discussed.The experimental results show that the NNT-ZNN can achieve relatively small error value compared to the ZNN.Corresponding to different activation functions,in first three applications of the above mentioned,the effects of various activation functions on the convergence rate of the NNT-ZNN model are discussed.It is founded that the hyperbolic sine and sign-bi-power functions result in better performance.Moreover,when the appropriate nonlinear activation function is used,the convergence time can be accelerated to a finite time.The simulation results can also been viewed as a guidepost for the researchers' future work.Among the above four applications,their solving difficulty is increasing step by step.For the given problem,the constructed four NNT-ZNN make success,and have good noise-tolerant performance.Combining all the experimental results,it can be said that the NNT-ZNN is effective,and robust to noise.