Set operations and order reductions for constrained zonotopes
Set operations and order reductions for constrained zonotopes
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DOI：
10.1016/j.automatica.2022.110204
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Vignesh Raghuraman;Justin P. Koeln
中科院分区：
文献类型：
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作者：
Vignesh Raghuraman;Justin P. Koeln
本文提出了使用零点和约束零点的方法来提高控制理论中常用的各种基于集合的运算的实用性。所提出的方法扩展了约束区域映射的使用，以表示由半空间交集、凸壳、稳健正不变集和庞特里亚金差分等操作产生的集合。还提出了降阶技术，它提供了较低复杂度的区域映射和约束区域映射的内近似。数值算例验证了基于区域区域的集合表示法在动态系统分析和控制中的有效性和计算优势。
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.