有限值终态递归神经网络计算

摘要/Abstract

摘要： 通常的递归神经网络计算方法采用渐近收敛的网络模型,误差函数渐近收敛于零,理论上需经过无穷长的计算时间才能获得被求解问题的精确解。文中提出了一种终态递归神经网络模型,该网络形式新颖,具有有限时间收敛特性,用于解决时变矩阵计算问题时可使得计算过程快速收敛,且计算精度高。该网络的另一特点是动态方程右端函数值有限,易于实现。首先,分析渐近收敛网络模型在时变计算问题求解方面的缺陷,说明引入终态网络模型的必要性;然后,给出终态网络动态方程,推导出该网络收敛时间的具体表达式。对于时变矩阵逆和广义逆求解,定义一个误差函数,并依据误差函数构造终态递归神经网络进行求解,使计算过程在有限时间内收敛便能得到精确解。在将任意初始位置下的冗余机械臂轨迹规划任务转换为二次规划问题后,利用所提出的神经网络进行计算,得出的关节角轨迹导致末端执行器完成封闭轨迹跟踪,且关节角严格返回初始位置,以实现可重复运动。使用MATLAB/SIMULINK对时变矩阵计算问题和机器人轨迹规划任务分别进行仿真,通过比较分别采用渐近网络模型和终态网络模型时的计算过程与结果可以看出,使用终态网络模型的计算过程收敛快且显著提高了计算精度。对不同时变计算问题的求解体现了所提神经网络的应用背景。

关键词: 工业机器人, 广义逆, 轨迹规划, 矩阵逆, 终态神经网络

Abstract: Conventional computing methods,by using recurrent neural networks,ensure the asymptotic convergence of the computing error such that the error converges to zero and the exact solution can be obtained as time approaches infinity.In this paper,a novel model of terminal recurrent neural networks was presented to address online computation problems arising from time-varying matrices.Such kind of network model is of the characteristics of the limited values of the right-hand side function and the finite settling time.Firstly,the shortcoming of asymptotically convergent network models in solving time-varying computational problems is analyzed,and the necessity of introducing the terminal network models is given.Then,the dynamics of the terminal network is characterized with the derivation for the expression of the settling time.For solving the problems of inverse and genera-lized inverses of time-varying matrices,an error function is defined,a terminal recurrent neural network is constructed based on the error function,so that the accurate solution can be achieved.For the path planning of industrial manipulators,the end effector tracks the closed trajectory by applying the terminal neural network,the joint angle returns to the initial position,and the repetitive motion is conducted in the presence of arbitrary initial position.MATLAB/SIMULINK is used for simulation of solving time-varying matrix computing problems and trajectory planning tasks of manipulators.By comparing the results obtained by the asymptotic network and the terminal network,it can be seen that the computing process using the terminal network converges in finite time and the computing accuracy is improved significantly.The presented solutions for different time-varying computing problems exhibit the applicability of the proposed terminal networks.

Key words: Generalized inverses, Industrial manipulators, Inverse matrix, Path planning, Terminal neural networks

中图分类号:

TP18

孙明轩,翁丁恩,张钰. 有限值终态递归神经网络计算[J]. 计算机科学, 2020, 47(1): 212-218. https://doi.org/10.11896/jsjkx.181001898

SUN Ming-xuan,WENG Ding-en,ZHANG Yu. Time-variant Neurocomputing with Finite-value Terminal Recurrent Neural Networks[J]. Computer Science, 2020, 47(1): 212-218. https://doi.org/10.11896/jsjkx.181001898

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