论文标题
具有输入延迟的离散时间线性系统的受控不变集的可扩展计算
Scalable Computation of Controlled Invariant Sets for Discrete-Time Linear Systems with Input Delays
论文作者
论文摘要
在本文中，我们首先提出了一种可以有效地计算出具有纯延迟输入的离散时间线性系统的最大鲁棒控制不变设置的方法。该方法的关键是要考虑原始系统的相同状态空间维度构建辅助线性系统（不延迟），并将辅助系统的最大不变集与原始系统的最大不变集相关联。当系统受到干扰时，确保安全性的安全性更难。在这些情况下，能够合并有关干扰的任何其他信息变得更加重要。在本文的第二部分中，我们概括了所提出的方法，以考虑到有关干扰的其他预览信息，同时保持计算效率。与通过延迟输入和预览的干扰添加状态空间来构建更高维系统的天真方法相比，提出的方法可以随着延迟时间的增加而缩放得多。
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system (without delay) with the same state-space dimension of the original system in consideration and to relate the maximal invariant set of the auxiliary system to that of the original system. When the system is subject to disturbances, guaranteeing safety is harder for systems with input delays. Ability to incorporate any additional information about the disturbance becomes more critical in these cases. Motivated by this observation, in the second part of the paper, we generalize the proposed method to take into account additional preview information on the disturbances, while maintaining computational efficiency. Compared with the naive approach of constructing a higher dimensional system by appending the state-space with the delayed inputs and previewed disturbances, the proposed approach is demonstrated to scale much better with the increasing delay time.
