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

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。

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.