求解时变线性不等式离散算法的设计与分析

提出一种用于求解时变线性不等式的数值算法.通过引入一个时变向量(其每个元素都大于或等于零),将时变线性不等式转化为一个时变矩阵向量方程,并给出用于求解该方程的连续时间模型(即神经网络).采用欧拉差分公式将其离散化,推导得到相应的离散算法,并通过理论分析和数值实验验证该离散算法的有效性.结果表明:所提出的离散算法的稳态误差(SSRE)具有O(τ²)的变化规律,当τ的数值减小10倍,算法的稳态误差可减小100倍.

Design and Analysis of Discrete Algorithm for Time-Varying Linear Inequality Solving

A numerical algorithm for time-varying linear inequality solving is proposed. By introducing a time-varying vector(of which each element is greater than or equal to zero), we convert the time-varying linear inequality to a time-varying matrix-vector equation. A continuous-time model(i.e., the neural network)is then presented to solve such an equation. Using Euler’s difference formula to discretize the continuous-time model, we propose the corresponding discrete algorithm. Both theoretical analysis and numerical results further substantiate the efficacy of such algorithm. These results also indicate that the steady-state residual error(SSRE)of the proposed discrete algorithm changes in an O(τ²)manner with being τ the sampling gap; when the τ value decreases by 10 times, the SSRE reduces by 100 times.