Fundamental Limits on Disturbance Propagation in Virtual Viscoelastic-based Multi-Agent Systems
Fundamental Limits on Disturbance Propagation in Virtual Viscoelastic-based Multi-Agent Systems
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DOI：
10.1109/med59994.2023.10185864
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Dinesh Murugan;Rozhin Hajian;Milad Siami
中科院分区：
文献类型：
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作者：
Dinesh Murugan;Rozhin Hajian;Milad Siami
本文研究了外生随机干扰下相称分数阶一致网络的性能退化问题。我们利用卡普托导数和拉普拉斯变换建立了网络动力学的分数阶微分方程，并采用动力系统的H2范数作为性能度量。通过开发一种图论方法，我们将底层图的结构规范与性能度量联系起来，并明确量化分数阶共识网络中最佳可实现性能水平的基本限制。我们还在网络的稀疏性和性能度量之间建立了新的联系，描述了揭示两者之间相互作用的基本权衡。最后，我们提供了数值实例来验证我们的理论结果，这可以帮助设计存在干扰的鲁棒分数阶控制系统。
In this paper, we investigate the performance deterioration of commensurate fractional-order consensus networks under exogenous stochastic disturbances. We formulate fractional-order differential equations for the network dynamics using Caputo derivatives and the Laplace transform, and employ the H2 norm of the dynamical system as a performance measure. By developing a graph-theoretic methodology, we relate the structural specifications of the underlying graphs to the performance measure and explicitly quantify fundamental limits on the best achievable levels of performance in fractional-order consensus networks. We also establish new connections between the sparsity of the network and the performance measure, characterizing fundamental tradeoffs that reveal the interplay between the two. Finally, we provide numerical illustrations to verify our theoretical results, which could help in the design of robust fractional-order control systems in the presence of disturbances.