论文标题
描述线性离散时间系统的控制能力的分析因素
Analytical Factors for Describing the Control Ability of Linear Discrete-time Systems
论文作者
论文摘要
在本文中，首先讨论由矩阵对产生的分析量计算，该分析量计算与$ n $不同或重复的真实特征值生成的分析量计算，然后首先讨论通过解构体积计算方程，构建了3类形状因子。这些分析量和形状因子可以准确地描述地位的大小和形状。因为基于对体积和形状因子的体积和形状因子的这些分析表达式，可以方便地量化了具有单位输入变量的LDT系统具有单位输入变量（即输入变量为1）的控制能力（即输入变量为1）直接相关。通过选择这些分析表达式作为目标函数或约束条件，可以建立一种新颖的优化问题和解决控制能力的方法。根据优化，不仅可以根据纸张\ cite {zhaomw202003}的结论来促进基于开环控制能力，而且还可以促进一些闭环控制性能，例如最佳的时间浪费，控制策略的鲁棒性，等等。
In this paper, the analytical volume computations of the zonotopes generated by the matrix pair with $n$ different or repeated real eigenvalues are discussed firstly, and then by deconstructing the volume computing equations, 3 classes of the shape factors are constructed. These analytical volume and shape factors can describe accurately the size and shape of the zonotopes. Because the control ability for LDT systems with the unit input variables (i.e. the input variable is with bounded value as 1) is directly related to the controllability region \cite{zhaomw202003}, based on these analytical expressions on the volume and shape factors, the control ability can be quantized conveniently. By choosing these analytical expressions as the objective function or constraint conditions, a novel optimizing problems and solving method for the control ability can be founded. Based on the optimization, not only the open-loop control ability, and but also the some closed-loop control performance, such as the optimal time waste, robustness of the control strategy, etc, can be promoted, according to the conclusions in paper \cite{zhaomw202003}.
