Title: Structural Controllability of Drift-free Bilinear Systems on $\mathbb{SE(n)}$ Show Chinese title

Title: 无漂移双线性系统的结构可控性$\mathbb{SE(n)}$

Abstract: We obtain graph theoretic necessary and sufficient conditions for the structural controllability of drift free bilinear systems on the special Euclidean group leveraging results from the existing literature. The graph theoretic conditions allow us to check the structural controllability in polynomial time. We use these conditions to find the sparsest structures for structural controllability. These conditions can also be used to check the structural accessibility of bilinear systems with drift. Equivalent conditions using the permutation group are also obtained. We consider the problem of link failures within a given structure and obtain equivalent conditions for structural controllability which are polynomial time checkable. We show that the problem of finding sparsest structures under $k$ link failures is NP-hard for $k>0$. We also discuss the case of structural controllability under probabilistic link failures. Show Chinese abstract

Abstract: 我们通过利用现有文献中的结果，得到了无漂移双线性系统在特殊欧几里得群上的结构能控性的图论必要和充分条件。 图论条件使我们能够在多项式时间内检查结构能控性。 我们使用这些条件来找到结构能控性的最稀疏结构。 这些条件也可以用来检查具有漂移的双线性系统的结构可达性。 还获得了使用置换群的等价条件。 我们考虑给定结构内的链路故障问题，并得到了结构能控性的等价条件，这些条件可以在多项式时间内检查。 我们证明了在$k$链路故障下寻找最稀疏结构的问题对于$k>0$是NP难的。 我们还讨论了在概率链路故障下的结构能控性情况。