A CHARACTERIZATION OF NETWORK PERFORMANCE: THE ROLE OF COMMUNICATION DIRECTIONALITY AND SYSTEM HETEROGENEITY
Johns Hopkins University
Networked dynamical systems’ ability to preserve the system equilibrium in the face of disruptive events or persistent disturbances can be an indication of the convergence efficiency and quantified as a measure of system performance. The performance analysis is usually facilitated by simplifications overlooking certain structural properties of the network that can potentially be significant to actual system behavior. We characterize the performance of networks in relation to these properties, such as communication directionality and system heterogeneity, and unravel their influence on overall performance. We examine performance metrics that quantify an aggregate system effort to maintain and/or restore a network equilibrium; formulated by a general quadratic function (L2 norm) of the system output. Using this approach, which builds on the widely-used H2 norm based analysis, we obtain novel closed-form solutions to the performance metrics. We then use them to identify the role of communication directionality and system heterogeneity in network performance. Particularly, we show that the effect of communication directionality on performance can be characterized by the spectral properties of the weighted Laplacian matrix describing the network interconnection and the output performance matrix. Our results indicate that while this directionality can degrade performance, well-designed feedback can also exploit directionality in certain cases to mitigate this degradation or even lead to improved performance. We also demonstrate that performance is sensitive to the degree of connectivity in networks with directed interconnection, however it does not necessarily improve by increasing this degree of connectivity. We then derive the asymptotic behavior of performance with respect to network size, and identify additional performance trade-offs associated with large-scale networks with communication directionality. In addition, we investigate system heterogeneity in droop-controlled inverter-based power systems, by relaxing the common assumption of uniformity of inverter control gains. This heterogeneity, which can result from the distribution of power demand between the inverters, can lead to performance limitations. Numerical examples verify and support our theoretical findings. Our results highlight the performance capabilities and limitations due to the structural properties of the network, and can inform judicious feedback design.
Networked Dynamical Systems, Network Analysis, Performance Metrics, Directed Graph, Digraph, Power Grid, Spatially Invariant System