Excitation Conditions for Uniform Exponential Stability of the Cooperative Gradient Algorithm Over Weakly Connected Digraphs
Excitation Conditions for Uniform Exponential Stability of the Cooperative Gradient Algorithm Over Weakly Connected Digraphs
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DOI：
10.1109/lcsys.2021.3049153
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发表时间：
2022
影响因子：
3
通讯作者：
M. Javed;J. Poveda;Xudong Chen
中科院分区：
文献类型：
--
作者：
M. Javed;J. Poveda;Xudong Chen
在这篇文章中，我们研究了具有持续激励（PE）节点和协作估计动态的网络上的鲁棒自适应参数估计问题。对于这一问题，众所周知，对于无向连接图网络，可以在一个合作的PE条件下建立一致指数稳定性（UES）的性质，该条件放宽了自适应控制中传统使用的标准个体PE假设。然而，在一般有向图中是否也可以使用类似的合作PE条件是一个悬而未决的问题。我们通过刻画一个广义的合作PE条件给出了这个问题的答案，该条件被证明是任意弱连通有向图上的合作梯度动力学演化中UES的充分必要条件。我们还为分布式学习动力学导出了一个类似的基于数据的广义合作条件，该条件使用记录数据而不是持续激励信号。我们进一步提出了研究动力学收敛速率的数值实验。
In this letter, we study the problem of robust adaptive parameter estimation over networks with persistently exciting (PE) nodes and cooperative estimation dynamics. For this problem, it is well known that for networks characterized by undirected connected graphs, the property of uniform exponential stability (UES) can be established under a cooperative PE condition that relaxes the standard individual PE assumptions traditionally used in adaptive control. However, it is an open question whether similar cooperative PE conditions can also be used in general directed graphs. We provide an answer to this question by characterizing a generalized cooperative PE condition that is proved to be necessary and sufficient for UES in cooperative gradient dynamics evolving over arbitrary weakly connected digraphs. We also derive a similar generalized cooperative data-based condition for distributed learning dynamics that use recorded data instead of persistently exciting signals. We further present numerical experiments that study the rates of convergence of the dynamics.