连续时间系统的组合不变性：从光滑性到Lebesgue密度

中文摘要 AI 辅助

这项工作建立了首个双向组合不变性结果：全局笛卡尔积集的鲁棒前向不变性被证明等价于每个局部子系统在来自其邻居的耦合输入下的鲁棒前向不变性。为此，我们引入了切向Lebesgue密度的概念，这是一个比经典光滑性更弱但足以保证各独立切锥的乘积等于乘积集的切锥的新条件。这种等价性降低了维度灾难的影响，允许将高维全局系统的验证分解为一系列局部子检查。该框架的可扩展性通过一个直流微电网数值示例得到展示，确认了验证复杂度仅随子系统数量线性增长。

英文摘要

This work establishes the first bidirectional compositional invariance result: robust forward invariance of a global Cartesian product set is shown to be equivalent to robust forward invariance of each local subsystem under coupling inputs from its neighbors. To facilitate this, we introduce the notion of tangential Lebesgue-density, a new condition that is weaker than classical sleekness but sufficient to ensure that the product of individual tangent cones equals the tangent cone of the product set. This equivalence reduces the curse of dimensionality by allowing the verification of a high-dimensional global system to be decomposed into a series of local sub-checks. The framework's scalability is demonstrated through a DC microgrid numerical example, confirming that the verification complexity grows only linearly with the number of subsystems.

发表机构

• College of Computing, University Mohammed VI Polytechnic (UM6P)（Mohammed VI Polytechnic大学计算学院）
• Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）
• CNRS（法国国家科学研究中心）
• Grenoble INP（格勒诺布尔国立理工学院）
• Laboratory of Signals and Systems (L2S)（信号与系统实验室）
• CentraleSupélec（中央理工-高等电力学院）
• Paris-Saclay University（巴黎萨克雷大学）

机构由 AI 辅助整理，请以论文原文为准。