[目的]为了求解时变复数西尔维斯特方程(Sylvester equation),提出两种全新的复值模糊归零神经网络(fuzzy logic system for zeroing neural network,FLSVZNN)模型.[方法]首先,在两种复数归零神经网络(com-plex-valued zeroing neural network,CVZNN)模型的基础上,引入模糊逻辑系统(fuzzy logic system,FLS)来控制信号的处理,从而提出两种FLSVZNN模型;然后,利用李亚普诺夫定理(Lyapunov's theorem)来分析模型的稳定性和收敛速度;最后,通过仿真试验来进一步验证FLSVZNN的优越性能.[结果]在求解时变复数西尔维斯特方程时,相比传统的神经网络模型,使用改进的符号双幂(sign-bi-power,SBP)函数来激活的FLSVZNN模型具有更好的收敛性和稳定性,可使误差函数在0.3 s左右收敛至0.[结论]本研究提出的两种FLSVZNN模型能快速求解时变复数西尔维斯特方程,这可为神经网络模型的建立及工程应用提供参考.
On fuzzy zeroing neural network algorithm for computing time-varying complex numbers
[Objective]In order to solve the time-varying complex Sylvester equation,two new fuzzy logic system for zeroing neural network(FLSVZNN)models were proposed.[Method]First,on the basis of two complex-valued zeroing neural network(CVZNN)models,the fuzzy logic system(FLS)was introduced to control signal processing,thus obtaining two FLSVZNN models;then,Lyapunov's theorem was used to analyze the stability and convergence rate of the models;finally,the superior performance of FLSVZNN was further verified by simulation experiments.[Result]When solving the time-varying complex Sylvester equation,compared with the traditional neural network model,the FLSVZNN models activated by the improved sign-bi-power(SBP)function boast better convergence and stability,which can make the error function converge to 0 in 0.3 seconds.[Conclusion]Two FLSVZNN models proposed in this study can quickly solve the time-varying complex Sylvester equation,which can provide references for the establishment of neural network models and engineering applications.
complex-valued zeroing neural networkfuzzy logic systemfinite-time convergenceactivation function
万方数据
维普
