论文标题
黑色框开关线性系统的数据驱动的不变子空间标识
Data-driven invariant subspace identification for black-box switched linear systems
论文作者
论文摘要
我们提出了一个算法框架，用于识别开关线性系统的候选不变子空间。也就是说，该框架允许根据有限的一组观察到的一步轨迹并具有先验置信度的有限的一个正顺序基础，其中系统的矩阵接近三角形矩阵。不变子空间的存在与系统矩阵的常见块三角形之间的联系是众所周知的。在系统上的某些假设下，当矩阵接近三角形时，也可以推断出不变子空间的存在。我们的方法依赖于方案优化中的二次lyapunov分析和最新工具。我们在共识和意见动态问题上提出了两种结果的应用；第一个允许在开关隐藏网络中识别断开的组件，而第二个则标识了具有拮抗交互的八卦过程的固定意见向量。
We present an algorithmic framework for the identification of candidate invariant subspaces for switched linear systems. Namely, the framework allows to compute an orthonormal basis in which the matrices of the system are close to block-triangular matrices, based on a finite set of observed one-step trajectories and with a priori confidence level. The link between the existence of an invariant subspace and a common block-triangularization of the system matrices is well known. Under some assumptions on the system, one can also infer the existence of an invariant subspace when the matrices are close to be block-triangular. Our approach relies on quadratic Lyapunov analysis and recent tools in scenario optimization. We present two applications of our results for problems of consensus and opinion dynamics; the first one allows to identify the disconnected components in a switching hidden network, while the second one identifies the stationary opinion vector of a switching gossip process with antagonistic interactions.
