Optimization of the $H_\infty$-norm of Dynamic Flow Networks

Johansson, Alexander; Wei, Jieqiang; Johansson, Karl Henrik; Chen, Jie

doi:10.48550/arxiv.1710.03154

Cited by 2 publications

(2 citation statements)

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“…In this direction, as the size of the plant (network) increases and the interactions become more sophisticated, having a knowledge about the the network structure can help us to address the resilience and robustness of such complex systems more efficiently. In this direction, there has been a vast literature in analyzing the effect of network structure on both system H 2 , [2,26,30] , and H ∞ performances [14,18,28]. Via combining the system-theoretic notions with algebraic graph theory, some papers have looked at these performance metrics as network centrality measures and discussed the control node (leader) selection problems in a given large-scale network to optimize each performance metric [8,18,25].…”

Section: Introductionmentioning

confidence: 99%

A Graph-Theoretic Approach to the $\mathcal{H}_{\infty}$ Performance of Dynamical Systems on Directed and Undirected Networks

Pirani¹,

Johansson²

2018

Preprint

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We study a graph-theoretic approach to the H∞ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system H∞ norm of the leader following dynamics and show the tightness of the proposed bounds. Then, we discuss the relation between the system H∞ norm for directed and undirected networks for specific classes of graphs, i.e., balanced digraphs and directed trees. Moreover, we investigate the effects of adding directed edges to a directed tree on the resulting system H∞ norm. In the end, we apply these theoretical results to a reference velocity tracking problem in a platoon of connected vehicles and discuss the effect of the location of the leading vehicle on the overall H∞ performance of the system.

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Section: Introductionmentioning

confidence: 99%

A Graph-Theoretic Approach to the $\mathcal{H}_{\infty}$ Performance of Dynamical Systems on Directed and Undirected Networks

Pirani¹,

Johansson²

2018

Preprint

Self Cite

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“…This condition does not play a prominent role here, but efficient stability checks would be needed for controller design. Other applications for H ∞ -norm minimization arise in the optimization of dynamic flow networks [9], parameter identification [18], and model reduction [17].…”

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confidence: 99%