确保采样线性系统可达性属性的切换规则综合
Synthesis of Switching Rules for Ensuring Reachability Properties of Sampled Linear Systems
AI总结：
针对周期采样分段线性动力学系统，提出间接抽象为有限离散事件系统和直接在连续状态空间上工作的两种方法，综合切换规则以确保系统始终停留在给定区域，并通过DC-DC升压转换器案例验证。
摘要：
我们考虑具有分段线性动力学的系统，这些系统以给定周期τ进行周期采样。在每个采样时刻，可以根据切换规则切换系统的模式，即线性动力学的参数。此类系统可以建模为混合自动机的一种特殊形式，称为“切换系统”，即具有无限实状态空间的自动机。问题是找到一个切换规则，保证系统在下一个采样时刻仍处于给定区域V中，并以此类推无限进行。在本文中，我们将考虑两种方法：间接方法将系统抽象为有限离散事件系统的形式，直接方法在连续状态空间上工作。我们的方法基于先前的工作，但我们将它们专门化到简化的上下文（线性、周期性切换时刻、无控制输入），这是由聚焦案例研究的特征所驱动的：由电子实验室SATIE（ENS Cachan）构建的DC-DC升压转换器。我们改进的方法使我们能够成功处理这个实际例子。
英文摘要：
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period τ . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a switching rule. Such systems can be modelled as a special form of hybrid automata, called "switched systems", that are automata with an infinite real state space. The problem is to find a switching rule that guarantees the system to still be in a given area V at the next sampling time, and so on indefinitely. In this paper, we will consider two approaches: the indirect one that abstracts the system under the form of a finite discrete event system, and the direct one that works on the continuous state space. Our methods rely on previous works, but we specialize them to a simplified context (linearity, periodic switching instants, absence of control input), which is motivated by the features of a focused case study: a DC-DC boost converter built by electronics laboratory SATIE (ENS Cachan). Our enhanced methods allow us to treat successfully this real-life example.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
