计算机科学 ›› 2024, Vol. 51 ›› Issue (8): 324-332.doi: 10.11896/jsjkx.230500052
李杏, 仲国民
LI Xing, ZHONG Guomin
摘要： 文中提出了具有对数调节时间的固定时间收敛递归神经网络(Recurrent Neural Network,RNN)模型,用于求解时变矩阵计算问题。设计并详细分析了两个新颖的RNN模型,推导出在给定初始条件下模型调节时间函数的精确表达式;并给出任意初始条件下调节时间函数的上界。相比现有的固定时间收敛的RNN模型,两个新颖的模型具有对数调节时间,其调节时间上界更小,收敛速度更快。考虑到初始误差实际上在一个有界的区域内,给出RNN模型半全局对数调节时间函数,并由此推导出半全局意义上的调节时间函数的上界。采用RNN模型半全局调节时间上界的倒数,提出半全局预定时间收敛到精确解的改进RNN模型,其预定时间是一个可调参数。给出了所提RNN模型对时变Lyapunov方程和时变Sylvester方程求解的仿真结果,并将其应用于具有初始误差的冗余机械臂的重复运动规划,进一步验证了所提RNN模型的有效性。
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