We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only to belong to a certain family due to a possibly inexact quantification of some parameters. By exploiting a set of realizations of those undetermined parameters, verifying the controlled invariance property of the given set amounts to a linear program, whose feasibility allows us to establish an a-posteriori probabilistic certificate on the controlled invariance property of such a set with respect to the nominal linear time-invariant dynamics. The proposed framework is applied to the control of a networked multi-agent system with unknown weighted graph.

中文翻译：

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一类黑箱线性系统的概率稳定性证书

对于一类黑箱线性系统，我们提供给定集合的受控不变性的样本外证书。具体来说，我们考虑线性时不变模型，由于某些参数的量化可能不精确，其状态空间矩阵仅属于某个族。通过利用这些未确定参数的实现集，验证给定集合的受控不变性等于线性程序，其可行性使我们能够针对该集合的受控不变性建立后验概率证明。标称线性时不变动力学。所提出的框架适用于具有未知加权图的网络化多智能体系统的控制。