Polytope shaping while preserving invariance
Polytope shaping while preserving invariance
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DOI：
10.1109/cdc51059.2022.9992851
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
N. Athanasopoulos
中科院分区：
文献类型：
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作者：
N. Athanasopoulos
我们提出了一个框架，如何动态地改变形状的不变多面体通过初等运算，即通过添加一个顶点或线性不等式在他们的描述，并在同一时间保持不变。我们研究了多面体的面格，并引入了锥格，它以一种有效的方式嵌入了多面体的几何结构和组合结构。结合以上，我们可以先验地描述由任一初等运算产生的集合的复杂性。重要的是，使用序理论的参数，我们确定的部分面和锥晶格，必须重新计算在每个操作。最后，我们回顾和推广了几个动力系统族的多面体保持不变性的等价代数条件。
We present a framework on how to dynamically change the shape of invariant polytopes via elementary operations, namely, by adding a vertex or a linear inequality in their description, and at the same time maintain invariance. We work on the face lattice of the polytope, and introduce the cone lattice which embeds in an efficient way the geometric and combinatorial structure of the polytope. Combining the above, we can characterize a priori the complexity of the set resulting from either elementary operation. Importantly, using order-theoretic arguments, we identify the parts of the face and cone lattice that must be recalculated in every operation. Finally, we recall and extend equivalent algebraic conditions for preserving invariance of polytopes for a few families of dynamical systems.