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arXiv 2001.07006eess.SYcs.SYmath.OC
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时变图上的分布式状态估计:利用信息量

Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information

Aritra Mitra, John A. Richards, Saurabh Bagchi, Shreyas Sundaram

摘要:

研究了时变通信图上LTI系统的分布式观测器设计问题。有限的现有工作对这一主题施加了各种限制的观察模型或通信图的序列。相比之下,我们提出了一个单一的时间尺度分布式观测器,在温和的假设下工作。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性,这些间隔甚至可以随着时间的推移无限增长。我们表明,在适当的条件下,约束这样的间隔的增长,联合可观性是足够的跟踪状态的任何离散时间LTI系统的指数快速,在任何期望的速度。事实上,我们还建立了有限时间收敛的基础上,我们的方法。最后,我们开发了一种算法的变体,该算法可证明对最坏情况的对抗性攻击具有鲁棒性,前提是图的序列随着时间的推移而充分连接。我们的方法的关键是“新鲜度指数”的概念,它跟踪整个网络中传播的信息的年龄。这样的指数使节点拒绝陈旧的状态估计,并反过来,有助于稳定的误差动态。

英文摘要:

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.

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