本文旨在量化一类受外源噪声影响的共识寻求多智能体网络中聚集波动的度量。此类噪声由具有厚尾概率分布的随机测度生成。我们定义累积尺度参数，作为输出变量概率分布尺度参数的度量，以衡量聚集波动。尽管此类度量在稳态下可以隐式地用闭式表达式表示，但一般情况下难以用网络参数显式表示。我们获得了几种基于拉普拉斯谱和输入噪声统计的可处理上界。我们的结果表明，依赖于基于高斯的最优设计算法将导致在由非高斯噪声输入驱动的网络中非最优的解决方案。该手稿已提交至IEEE Transactions on Control of Network Systems发表。它是2018年美国控制会议论文集中的初步论文的扩展版本。
英文摘要：
The focus of this paper is to quantify measures of aggregate fluctuations for a class of consensus-seeking multiagent networks subject to exogenous noise with alpha-stable distributions. This type of noise is generated by a class of random measures with heavy-tailed probability distributions. We define a cumulative scale parameter using scale parameters of probability distributions of the output variables, as a measure of aggregate fluctuation. Although this class of measures can be characterized implicitly in closed-form in steady-state, finding their explicit forms in terms of network parameters is, in general, almost impossible. We obtain several tractable upper bounds in terms of Laplacian spectrum and statistics of the input noise. Our results suggest that relying on Gaussian-based optimal design algorithms will result in non-optimal solutions for networks that are driven by non-Gaussian noise inputs with alpha-stable distributions.
The manuscript has been submitted for publication to IEEE Transactions on Control of Network Systems. It is the extended version of preliminary paper included in the proceedings of the 2018 American Control Conference.
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