用于时变矩阵计算的固定时间递归神经网络及其在重复运动规划中的应用  

Fixed-time Recurrent Neural Networks for Time-variant Matrix Computing and Its Application in Repeatable Motion Planning

作　　者：李杏 仲国民[1] LI Xing;ZHONG Guomin(College of Information Engineering,Zhejiang University of Technology,Hangzhou 310023,China)

机构地区：[1]浙江工业大学信息工程学院,杭州310023

出　　处：《计算机科学》2024年第8期324-332,共9页Computer Science

基　　金：国家自然科学基金(62073291)。

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。Fixed-time recurrent neural network(RNN)models with logarithmic settling time are proposed for solving time-variant neural computing problems.Two novel RNN models are designed and analyzed in detail,deriving the explicit expressions of settling time functions and providing the upper bounds of the settling times under any initial condition.Compared with the existing RNN models with fixed-time convergence,the two novel models with logarithmic settling time have a smaller upper bound on the settling time and faster convergence speeds.Taking into account initial conditions located within a region with a definite finite radius,the settling time functions of the RNN models with logarithmic settling time are given,and the upper bounds on the settling time functions in the semi-global sense are derived.Modified RNN models adopt the inverse of the bound to ensure that the semi-global predefined time converges to the exact solution,and its prescribed time is an adjustable parameter.Simulation results of the proposed RNN model for solving time-variant Lyapunov and Sylvester equations are given.The proposed RNNs are applied to the repetitive motion planning of a redundant manipulator with initial errors,and numerical results are presented to verify the effectiveness of the proposed RNN models.

关 键 词：时变神经计算 对数调节时间 固定/预定时间收敛 工业机器人 重复运动规划 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置]