求解时变非线性方程的Adams-Bashforth离散时间算法

Adams-Bashforth Discrete-Time Algorithm For Solving Time-Varying Nonlinear Equations

为了更好地解决时变非线性方程(time-varying nonlinear equation,TVNE),设计了一类Adams-Bashforth离散时间算法。首先给出了求解TVNE的连续时间零化神经网络,该神经网络具有指数收敛速度。然后利用线性多步算法将连续时间零化神经网络离散化,提出了一类六步Adams-Bashforth离散时间算法,并利用Jury稳定准则,给出了Adams-Bashforth离散算法步长的有效区间。最后将所提出的算法应用于解决机械臂路径规划问题,得到了较好的数值效果,精度最终可以达到10^(-14)m。

To better solve time-varying nonlinear equations(TVNE),this paper designs an Adams-Bashforth discrete-time algorithm.Specifically,we first give a continuous time zeroing neural network for TVNE,which has exponential convergence speed.Then,we use the linear multi-step algorithm to discretize the continuous time zeroing neural network,and propose a class of six step Adams-Bashforth discretization algorithm.Using the Jury stability criterion,we derive the effective interval of the step size of Adams-Bashforth discrete algorithm.Finally,the proposed algorithm is applied to solve the manipulator path planning problem,which results some encouraging results,and the accuracy can finally reach 10^(-14) meter.