We study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-time-scale distributed observer that works under mild assumptions. Specifically, our communication model only requires strong-connectivity to be preserved over non-overlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. In fact, we also establish finite-time convergence based on our approach. Finally, we develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a "freshness-index" that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.

中文翻译：

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时变图上的分布式状态估计：利用信息时代

我们研究了在时变通信图上为 LTI 系统设计分布式观察器的问题。关于该主题的有限现有工作对观察模型或通信图序列施加了各种限制。相比之下，我们提出了一个在温和假设下工作的单时间尺度分布式观察器。具体来说，我们的通信模型只需要在不重叠的连续间隔上保持强连接，甚至允许随着时间的推移无限增长。我们表明，在限制此类间隔增长的合适条件下，联合可观测性足以以任何所需的速率以指数方式快速跟踪任何离散时间 LTI 系统的状态。事实上，我们也基于我们的方法建立了有限时间收敛。最后，我们开发了一种算法变体，该变体可证明对最坏情况的对抗性攻击具有鲁棒性，前提是图序列随着时间的推移充分连接。我们方法的关键是“新鲜度指数”的概念，它跟踪通过网络传播的信息的年龄。这样的指数使节点能够拒绝对状态的过时估计，进而有助于误差动态的稳定性。