隐式-显式方法获得的网络：离散时间分布式中位数求解器
Networks obtained by Implicit-Explicit Method: Discrete-time distributed median solver
摘要：
为了使一致性算法对离群值具有鲁棒性，中值上的一致性最近引起了一些关注。它有其适用性，例如构建一个弹性的分布式状态估计。同时，大多数现有的工作考虑连续时间算法，并使用高增益和不连续的向量场。这就提出了显式方法离散化时需要较小的时间步长并产生抖振的问题。因此，在本文中，我们强调，这些问题消失时，我们利用隐式显式方法，为更广泛的一类网络设计的混合动力学方法。特别是，对于无向和连通图，我们提出了一个离散时间分布式中值求解器，不遭受抖振。我们还通过仿真验证，它具有较小的迭代次数所需的到达稳态。
英文摘要：
In the purpose of making the consensus algorithm robust to outliers, consensus on the median value has recently attracted some attention. It has its applicability in for instance constructing a resilient distributed state estimator. Meanwhile, most of the existing works consider continuous-time algorithms and uses high-gain and discontinuous vector fields. This issues a problem of the need for smaller time steps and yielding chattering when discretizing by explicit method for its practical use. Thus, in this paper, we highlight that these issues vanish when we utilize instead Implicit-Explicit Method, for a broader class of networks designed by the blended dynamics approach. In particular, for undirected and connected graphs, we propose a discrete-time distributed median solver that does not suffer from chattering. We also verify by simulation that it has a smaller iteration number required to arrive at a steady-state.
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