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Set operations and order reductions for constrained zonotopes
arXiv - CS - Systems and Control Pub Date : 2020-09-13 , DOI: arxiv-2009.06039
Vignesh Raghuraman, Justin P. Koeln

This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to represent sets resulting from operations including halfspace intersections, convex hulls, robust positively invariant sets, and Pontryagin differences. Order reduction techniques are also presented that provide lower-complexity inner-approximations of zonotopes and constrained zonotopes. Numerical examples are used to demonstrate the efficacy and computational advantages of using zonotope-based set representations for dynamic system analysis and control.

中文翻译:

约束带位的集合操作和降阶

本文介绍了使用带状环带和约束带带的方法,以提高控制理论中常用的各种基于集合的操作的实用性。所提出的方法扩展了约束带位的使用,以表示由包括半空间交集、凸包、稳健正不变集和庞特里亚金差异在内的操作产生的集合。还提出了降阶技术,这些技术提供了带状环带和受约束带带环的复杂度较低的内部近似值。数值示例用于证明使用基于区位的集合表示进行动态系统分析和控制的功效和计算优势。
更新日期:2020-09-15
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