A nonlinear time-varying system solving method based on a neural network

Abstract

The invention discloses a nonlinear time-varying system solving method based on a neural network, which comprises the following specific steps of: (1) formulating an actual engineering problem, and establishing a standard model of a nonlinear time-varying system required to be solved; (2) designing an error function based on the established standard model of the nonlinear time-varying system; (3)deriving the error function, and introducing a monotonically increasing odd activation function according to the standard model of the nonlinear time-varying system and the derivative of the error function; (4) designing a time-varying parameter, and establishing a variable-parameter recurrent neural network model according to the error function, the time-varying parameter and the activation function; And (5) solving the variable-parameter recurrent neural network to obtain a state solution which is the solution of the actual engineering problem. Based on a recurrent neural network model, themethod has global convergence characteristics when a nonlinear time-varying system is solved by applying linear equal activation functions and variable parameters, and errors can be converged to zeroat a hyper-exponential speed, so that the calculation speed is greatly increased.

Description

technical field [0001] The invention relates to the field of neural dynamics, in particular to a method for solving nonlinear time-varying systems based on neural networks. Background technique [0002] Nonlinear problems have an important impact on scientific research and engineering application practice. Many practical problems can be described as f(x)=0 and thus solved. But since state variables always evolve over time, computational methods need to be fast enough so that the computed solution can track the theoretical solution. In the past few decades, many researchers have devoted themselves to obtaining efficient, exact or approximate solutions for nonlinear time-varying systems, but because some nonlinear time-varying systems do not have exact analytical solutions, they can only be dealt with by numerical methods. Nonlinear time-varying systems. However, numerical methods are not efficient enough because they are performed in serial processing on digital computers....

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Problems solved by technology

However, when the calculation scale becomes larger, the time cost of GNN and ZNN calculation results will be higher

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