This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes – convex polytopes – through the addition of $N$ binary zonotope factors. The major contribution of this manuscript is a closed-form solution for exact forward reachable sets of discrete-time, linear hybrid systems modeled as mixed logical dynamical systems. The proposed approach captures the worst-case exponential growth in the number of convex sets required to represent the nonconvex reachable set while exhibiting only linear growth in the complexity of the hybrid zonotope set representation. Redundancy removal techniques are provided that leverage binary trees to store the combinations of binary factors of the hybrid zonotope that map to nonempty convex subsets. Numerical examples show the hybrid zonotope’s ability to compactly represent nonconvex reachable sets with an exponential number of features. Furthermore, the hybrid zonotope is shown to be closed under linear mappings, Minkowski sums, generalized intersections, and halfspace intersections.

这篇文章提出了一个新的集合表示，命名为hybrid zonotope，相当于 ${\mathrm{2个}}^{否}$约束环带形体——凸多形体——通过添加 $否$二元环带因子。这篇手稿的主要贡献是一个封闭形式的解决方案，用于精确前向可达的离散时间、线性混合系统建模为混合逻辑动力系统。所提出的方法捕​​获了表示非凸可达集所需的凸集数量的最坏情况指数增长，同时仅表现出混合 zonotope 集表示的复杂性的线性增长。提供了冗余去除技术，利用二叉树来存储映射到非空凸子集的混合环带的二元因子的组合。数值示例显示混合 zonotope 能够紧凑地表示具有指数数量的特征的非凸可达集。此外，混合环带显示在线性映射下是封闭的，