线性时变系统的过逼近可达管
Over-approximating reachable tubes of linear time-varying systems
摘要：
针对线性连续时变控制系统，当系统的初态和输入都服从紧凸不确定性时，提出了一种在紧时间区间上过逼近可达管的方法.该方法使用转移阵的数值逼近，是一阶收敛的，并假设有能力计算有限维的紧凑凸集。我们还提出了一个变体，适用于zonotopic的不确定性的情况下，只使用线性代数运算，并产生zonotopic过近似。后一种变体的性能证明了一个例子。
英文摘要：
We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic over-approximations. The performance of the latter variant is demonstrated on an example.
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