Research Of Complex Time-varying Matrix Inversion Based On Recurrent Neural Network

The time-varying matrix inversion has widely appeared in modern scientific research and engineering.Especially in the fields of automatic control and signal processing,solving time-varying calculations is a key step.Most of the existing methods for solving matrix inverses are numerical iterative methods that are suitable for static matrices.However,there are problems such as high time complexity and insufficient timeliness of calculation when these traditional methods are used to deal with matrices with time coefficients.On the other hand,with the deepening of research,many problems that appear in engineerings such as signal analysis,image processing,and robot control can be formulated as time-varying problems in the complex-number field,and the more common one is complex time-varying matrix inversion.Since the inversion of a complex time-varying matrix is more complicated than the inversion of a time-varying matrix in a real-number field,the current method of converting it into a real-number matrix equation requires more extra calculations.Therefore,the current method for solving the inverse of a complex time-varying matrix is not effective.The artificial neural network has become a powerful tool for information processing and optimization calculations due to its characteristics of self-learning,fast optimization,and approximation to any functions.Aiming at the inversion of complex time-varying matrices,the thesis designs a recurrent neural network-based solution model with model design,theoretical derivation and simulation verification as the main research content.The thesis first establishes the recurrent neural network model in coordinate form and exponential form based on the complex number arithmetic rules,and the convergence of the model is analyzed by using Lyapunov stability theory to ensure the effectiveness of the model.On this basis,the thesis improves the model's activation function design,combining the sign function,linear function,power function,and exponential function into special nonlinear activation functions to accelerate the model to finite-time convergence and constant time convergence.The superior convergence performance of the improved models is derived using the theory of neural dynamics method,and it is programmed on the MATLAB platform for simulation verification.In addition,referring to the design idea of the adaptive control system,the thesis adds three different adaptive parameters in the design of activation function and carries out rigorous theoretical analysis and simulation comparison experiments on the model with parameters,which proves that the adaptive parameters can effectively improve the convergence performance of the model.Compared with the existing complex recurrent neural network model,theoretical derivation and simulation experiment results show that the model proposed in this thesis has better convergence performance,faster convergence speed,and shorter convergence time.