We study the admissibility problem in multivariate algebraic systems, such as ac electrical networks, where the power injection is quadratic in the state. The goal of such systems is to ensure that the state stays in some security set (e.g., magnitudes of nodal voltages and branch currents are within safety bounds). A common practice is to implicitly control the state by controlling the injection; a difficulty is that the number of states that correspond to a given injection can be zero or many. Further, the injection is subject to some uncertainty. The admissibility problem is whether it is possible to ensure that the state stays in the security set, given that the only available information is some uncertainty set that constrains the injection. We extend the recently proposed V-control theory, design a solution framework to test if a given uncertainty set is admissible, and develop a concrete method for ac electrical networks.

中文翻译：

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二次代数系统中不确定注入的可容许性

我们研究了多元代数系统（例如ac电网）中的可容许性问题，在该系统中，功率注入在该状态下是二次方的。这种系统的目标是确保状态保持在某个安全集中（例如，节点电压和分支电流的大小在安全范围内）。常见的做法是通过控制注入来隐式控制状态。困难在于对应于给定喷射的状态数可以为零或很多。此外，注入存在一些不确定性。可取性问题是，假设唯一可用的信息是约束注入的某些不确定性集合，则是否有可能确保状态停留在安全性集合中。我们扩展了最近提出的V控制理论，