Sylvester时变矩阵方程求解的终态神经网络算法

doi:10.11896／j.issn.1002-137X.2018.10.038

计算机科学 ›› 2018, Vol. 45 ›› Issue (10): 207-211.doi: 10.11896／j.issn.1002-137X.2018.10.038

Sylvester时变矩阵方程求解的终态神经网络算法

孔颖^1,2, 孙明轩¹

浙江工业大学信息工程学院杭州310023 ¹
浙江科技学院信息与电子工程学院杭州310023 ²

收稿日期:2017-05-31 出版日期:2018-11-05 发布日期:2018-11-05
作者简介:孔颖(1980-),女,博士生,讲师,主要研究领域为神经网络、智能机械臂控制、模式识别,E-mail:kongying-888@163.com(通信作者);孙明轩(1961-),男,博士,教授,主要研究领域为迭代学习控制。
基金资助:
国家自然科学基金(61573320)资助

Terminal Neural Network Algorithm for Solution of Time-varying Sylvester Matrix Equations

KONG Ying^1,2, SUN Ming-xuan¹

College of Information Engineering,Zhejiang University of Technology,Hangzhou 310023,China ¹
School of Information and Electronic Engineering,Zhejiang University of Science and Technology,Hangzhou 310023,China ²

Received:2017-05-31 Online:2018-11-05 Published:2018-11-05

摘要/Abstract

摘要： 为了更好地提高收敛的速度和精度,提出一种终态神经网络(TNN)及其加速形式(ATNN)的求解方法。该网络求解方法具有终态吸引特性,能够在有限的时间内得到时变矩阵的有效解。相比于具有渐近收敛动态特性的神经网络,该神经网络方法具有有限时间收敛性,不仅能够改变收敛速度,而且能达到较高的收敛精度。将3种不同的神经网络方法用于求解时变Sylvester动态方程;同时,以终态神经网络求解二次优化问题,实现冗余机械臂Katana6M180有限时间收敛的重复运动规划任务。仿真结果验证了终态神经网络方法的有效性。

关键词: Sylvester时变矩阵方程, 有限时间收敛, 终态神经网络, 重复运动规划

Abstract: In order to improve the convergence rate and convergence precision,a method for new types of terminal neural network (TNN)and its accelerated form (ATNN)was proposed.This method has terminal attractor characteristics and can get effective solution for time-varying matrix in finite time.In contrast to the ANN,it’s proved that TNN can accelerate the convergence,speed and achieve finite-time convergence.It not only improves the rate of convergence,but also results in high computing precision.The dynamic equations of time-varying Sylvester are solved by ANN,TNN and ATNN models respectively.In addition,the terminal neural network models are applied in Katana6M180 manipulator to demonstrate the effectiveness of the proposed computing models in performing the repeatable motion planning tasks.The simulation results verify the validity of the terminal neural network method.

Key words: Finite-time convergence, Repeatable motion planning, Terminal neural networks, Time-varying Sylvester matrix equations

中图分类号:

TP391

孔颖, 孙明轩. Sylvester时变矩阵方程求解的终态神经网络算法[J]. 计算机科学, 2018, 45(10): 207-211. https://doi.org/10.11896／j.issn.1002-137X.2018.10.038

KONG Ying, SUN Ming-xuan. Terminal Neural Network Algorithm for Solution of Time-varying Sylvester Matrix Equations[J]. Computer Science, 2018, 45(10): 207-211. https://doi.org/10.11896／j.issn.1002-137X.2018.10.038

参考文献

[1]BARTELS R H,STEWART G W.Solution of the matrix equation AX+XB=C[J].Communications of the Acm,1972,15(9):820-826.
[2]LIU E D,JIN Y W,ZHANG S Y.Adaptive observer for nonli- near combinatorial systems based on dynamic neural networks[J].Control and Decision,2004,19(7):8764-8768.(in Chinese)
刘恩东,井元伟,张嗣瀛.基于动态神经网络的非线性组合系统自适应观测器[J].控制与决策,2004,19(7):8764-8768.
[3]ZHU R J,CAI T Y.The observer of nonlinear system based on dynamic neural networks[J].Information and Control,1998,27(6):421-425.(in Chinese)
朱瑞军,柴天佑.基于动态神经网络的非线性系统曾一棒观测器设计[J].信息与控制,1998,27(6):421-425.
[4]YANG J Y,JIA Y M.Adaptive observer for a class of nonlinear uncertain systems based on dynamic recurrent neural networks[J].Control and Decision,2002,17(1):81-91.(in Chinese)
杨晋勇,贾英民.基于动态递归神经网络的一类非线性不确定系统的自适应观测器[J].控制与决策,2002,17(1):89-91.[5]BAI J,LU R.Finite-time stability analysis of discrete-time fuzzy hopfield neural network[J].Neurocomputing,2015,159(2):263-267.
[6]CAO Y.Dynamic modeling and neural network adaptive control of a deployable manipulator system[J].Journal of Guidance Control & Dynamics,2015,29(1):192-195.
[7]ZHANG Y,CHEN D C,GUO D S.On exponential convergence of nonlinear gradient dynamics system with application to square root finding [J].Nonlinear Dynamics,2015,79(2):983-1003.
[8]LI S.Accelerating a recurrent neural netwok to finite-time convergence for solving time-varying sylvester equation by using a sign-bi-power activation function[J].Neural Processing Letters,2013,37(2):189-205.
[9]WANG J.Analysis and design of a recurrent neural networks for linear programming[J].IEEE Transactions on Circuits and Systems,1993,40(9):613-618.
[10]WHITNEY D E.Resolved motion rate control of manipulators and human prostheses[J].IEEE Transactions on Man Machine Systems,1969,10(2):467-453.
[11]POLVERINI M,ZANCHETTIN A.A computationally efficient safety assessment for collaborative robotics applications [J].Robotics and Computer-Integrated Manufacturing,2017,46:25-37.
[12]CHEN F T,SUN Y Y.Resolving manipulator redundancy under inequality constraints [J].IEEE Transactions on Robotics Automation,1994,10(1):65-71.
[13]JIN L,ZHANG Y N.Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamicsystem of linear equations[J].Neural Computing & Applications,2018,29(11):1217-1232.
[14]LI Z P,SHAO X Y,ZHANG D X,et al.Steering System Control Strategy Based on Overview of Automotive Electric Power[J].Journal of Chongqing Institute of Technology,2015,29(8):6-11.(in Chinese)
李志鹏,邵宪友,张东兴,等.基于BP神经网络的电控发动机故障诊断研究[J].重庆理工大学学报(自然科学),2015,29(8):6-11.

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Sylvester时变矩阵方程求解的终态神经网络算法

Terminal Neural Network Algorithm for Solution of Time-varying Sylvester Matrix Equations

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