Optimization of the $\mathcal{H}_{\infty}$-norm of Dynamic Flow Networks

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

doi:10.23919/acc.2018.8431398

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…Necessity. If the equilibrium point is hyperbolic, i.e., i 0 (J dyn ) = 0, then F is nonsingular by the relation between J dyn and F in (16). So L G has only one zero eigenvalue due to i 0 (L G ) = i 0 (F ) + 1.…”

Section: Definition 5 (Hyperbolicity Stability and Type Of Equilibriamentioning

confidence: 99%

“…Some bounds for the Laplacian spectrum are constructed by effective resistance in [14], which describe the convergence speed of distributed control. The H 2 norm and H ∞ norm of linear oscillator networks are given in terms of effective resistance in [15] and [16], respectively. In [17,18], the definition of effective resistance is extended from undirected graphs to directed graphs, which provides a new tool for control problems over directed graphs.…”

Section: Introductionmentioning

confidence: 99%

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On Extension of Effective Resistance With Application to Graph Laplacian Definiteness and Power Network Stability

Song

Hill

2019

IEEE Trans. Circuits Syst. I

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This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the traditional definitions that only apply to a pair of nodes. The monotonicity and convexity properties are preserved by the extended definitions. The extended definitions provide new insights into graph Laplacian definiteness and power network stability. It is proved that the Laplacian matrix of a signed graph is positive semi-definite with only one zero eigenvalue if and only if the effective conductances between some specific pairs of node sets are positive. Also the number of Laplacian negative eigenvalues is upper bounded by the number of negative weighted edges. In addition, new conditions for the small-disturbance angle stability, hyperbolicity and type of power system equilibria are established, which intuitively interpret angle instability as the electrical antagonism between certain two sets of nodes in the defined active power flow graph. Moreover, a novel optimal power flow (OPF) model with effective conductance constraints is formulated, which significantly enhances power system transient stability. By the properties of extended effective conductance, the proposed OPF model admits a convex relaxation representation that achieves global optimality.

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Section: Definition 5 (Hyperbolicity Stability and Type Of Equilibriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Extension of Effective Resistance With Application to Graph Laplacian Definiteness and Power Network Stability

Song

Hill

2019

IEEE Trans. Circuits Syst. I

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“…Previous work on dynamic flow networks typically focused on the nominal or the robust setting. Many results have been developed for disruption-free networks [12,13,14,15,16,17,18,19], which provide hints for the disruption-prone setting. Robust control strategies have been developed in response to physical (i.e.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Control of Dynamic Flow Networks Subject to Stochastic Cyber-Physical Disruptions

Tang,

Jin

2020

Preprint

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Modern network systems such as transportation, manufacturing, and communication systems are subject to cyber-physical disruptions. Cyber disruptions compromise sensing and/or actuating which closed-loop control relies on, and physical disruptions undermine network capability. This paper develops a novel approach to analysis and design of traffic control for dynamic flow networks subject to a rather broad class of disruptions. We consider a single-origin-single-destination acyclic network with possibly finite link storage spaces. Both cyber and physical disruptions are modeled as a set of discrete modes that modify the control and/or the network flow dynamics. The network switches between various modes according to a Markov process. By considering switched, piecewise polynomial Lyapunov functions and exploiting monotonicity of the network flow dynamics, we analyze network throughput under various disruption scenarios and show that cyber-physical disruptions can significantly reduce network throughput. For control design, we derive two results analogous to the classical maxflow min-cut theorem: (i) for a network with observable disruption modes, there exist mode-dependent controls that attain the expected-min-cut capacity; (ii) for a network with infinite link storage spaces, there exists an open-loop control that attains the minexpected-cut capacity. We also design a closed-loop control for general cases and derive an explicit relation from the control to a lower-bound for throughput. Our approach is illustrated by a series of numerical examples.

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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%