Design And Analysis Of Complex-Valued Zeroing Neural Network For Solving Time-Varying Complex-Valued Problems

In recent years,neural networks have become a research hotspot due to their high-performance parallel processing and simple circuit implementation.Scholars have proposed many different types of neural networks based on gradients to solve various mathematical problems.However,the existing neural networks all have a shortcoming,that is,they lack speed compensation for time-varying coefficients,which often fail to meet the requirements of the real engineering field.Therefore,they can only solve time-invariant problems and cannot handle time-varying problems well.With the deepening of research,a class of Zeroing Neural Network(ZNN)is proposed not only to solve time-varying and time-invariant problems,but also has the advantage of real-time and fast convergence performance.Since ZNN was put forward,it has been widely concerned and used to solve many real-valued problems.However,there are few studies on complex-valued problems.It is worth mentioning that the competitive advantages of complex-valued neural networks in many aspects have surpassed real-valued neural networks,and real-numbers are also a special kind of complex numbers.Therefore,this paper mainly uses the complex-valued ZNN to study three complex-valued problems,which are time-varying complex-valued Sylvester equations,dynamic complex-valued linear equations,and the Drazin inverse of complex-valued time-varying matrices.The method of processing complex values in this article is different from the traditional method,which convert complex values to real values and then process them.In this paper,two equivalent complex-value processing methods are used to directly process complex-values without converting complex-values into real-values.The first method is to process the real and imaginary parts of the complex-value at the same time,and the second method is to process the modulus of the complex-value.All in all,this paper focuses on the following aspects of work:(1)To solve the time-varying complex-valued Sylvester equation,develop and research an improved finite time zeroing neural network(IFTZNN),and the research significance and background of the Sylvester equation are analyzed.Based on two new complex-value processing methods,two IFTZNN models are proposed.In order to get a better convergence effect for the model,an excellent nonlinear activation function is used in the model.In addition,theoretical analysis and comparative simulation experiments are carried out on the IFTZNN model.(2)A new complex-valued zeroing neural network(NCZNN)is studied to solve a set of dynamic complex linear equations,and the significance of studying the equations is given.The paper also uses the SBP nonlinear activation function to enable the proposed NCZNN model to converge in a finite time.In addition,the NCZNN model is analyzed in detail according to two complex value processing methods,and the corresponding upper limit of convergence time is calculated.Two numerical experiments are carried out by using the NCZNN model and the original ZNN model,and the comparison results are finally proved.(3)Two nonlinear activation complex-valued zeroing neural networks(NACZNN)are studied to solve the Drazin inverse of the complex-valued time-varying matrix,and analyze the significance of this equation.In this paper,by comparing the original NACZNN model,using an improved activation function instead of the SBP function in the NACZNN model,and using numerical theoretical analysis to prove that it has a better finite time convergence and an upper bound on the convergence time.Finally,the computer simulation results further prove that the NACZNN model is better than the original NACZNN model.