Design And Analysis Of New Recurrent Neural Network Method For Time-varying Algebraic Problems

In order to accurately solve algebraic problems such as time-varying matrix inversion and time-varying Sylvester equation,In this dissertation,several new types of recurrent neural networks are proposed and studied on the basis of the original zeroing neural network model,and the convergence,stability and robustness of these models have been theoretically analyzed in detail.The corresponding numerical simulation results further verify the effectiveness and superiority of the proposed new recurrent neural network models.Specifically,this dissertation researches on the following aspects.1)A complex-valued nonlinear recurrent neural network is designed and researched for time-varying matrix inversion(TVMI)solving in complex field.Unlike the design methods of the conventional gradient neural network(CGNN)and the previous Zeroing neural network(ZNN),the proposed complex-valued nonlinear recurrent neural network(CVNRNN)model is established on basis of a nonlinear evolution formula and possesses a better finite-time convergence.Besides,the detailed theoretical analysis provides a guarantee for the finite-time convergence achievement of the CVNRNN model.In addition,the theoretical analysis is also verified by numerical simulations,which comparatively show that the proposed CVNRNN model is faster and more accurate than the ZNN model and the CGNN model in solving time-varying complex matrix inversion.2)In order to solve the problem that the neural network model is disturbed by noise in the hardware implementation process,a complex-valued noise-tolerant zeroing neural network(CVNTZNN)on the basis of an integraltype design formula is established and investigated for finding complex-valued TVMI under a wide variety of noises.Furthermore,both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved.For comparison and verification purposes,the existing ZNN and gradient neural network(GNN)have been presented to address the same problem under the same conditions.Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TVMI under various kinds of noises,by comparing the existing ZNN and GNN models.3)In order to realize the predefined-time convergence of the ZNN model and modify its robustness,two new noise-tolerant ZNNs(NNTZNN)are established by devising two novelly constructed nonlinear activation functions(AF)to find the accurate solution of the time-variant Sylvester equation in the presence of various noises.Unlike the original ZNN models activated by known AFs,the proposed two NNTZNN models are activated by two novel AFs,therefore,possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises.Besides,the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises.Simulation comparative results further verify the excellent performance of the proposed NNTZNN models,when applied to online solution of the time-variant Sylvester equation.4)Unlike the traditional fixed-parameter ZNN model(FPZNN),on the basis of the original varying parameter zeroing neural network(VPZNN)model,an improved varying parameter zeroing neural network(IVPZNN)is established and researched to solve the TVMI.Specifically,the value of the proposed novel time-varying parameter in IVPZNN model can grow rapidly over time,which will better meet the needs of ZNN in hardware implementation.In addition,theoretical analyses of the novel time varying parameter and the proposed IVPZNN model are given to guarantee the global super-exponential convergence and finite-time convergence.Numerical calculate results verify the superior property of the established IVPZNN model for calculating the TVMI problem,as compared with the previously existing FPZNN and VPZNN models.