We review selected results related to the robustness of networked systems in finite and asymptotically large size regimes in static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss the effect of physical constraints on robustness to loss in link capacities. In the dynamical setting, we review several settings in which small-gain-type analysis provides tight robustness guarantees for linear dynamics over finite networks toward worst-case and stochastic disturbances. We discuss network flow dynamic settings where nonlinear techniques facilitate understanding the effect, on robustness, of constraints on capacity and information, substituting information with control action, and cascading failure. We also contrast cascading failure with a representative contagion model. For asymptotically large networks, we discuss the role of network properties in connecting microscopic shocks to emergent macroscopic fluctuations under linear dynamics as well as for economic networks at equilibrium. Through this review, we aim to achieve two objectives: to highlight selected settings in which the role of the interconnectivity structure of a network in its robustness is well understood, and to highlight a few additional settings in which existing system-theoretic tools give tight robustness guarantees and that are also appropriate avenues for future network-theoretic investigations.
|Original language||English (US)|
|Number of pages||35|
|Journal||Annual Review of Control, Robotics, and Autonomous Systems|
|State||Published - May 3 2020|
Bibliographical noteKAUST Repository Item: Exported on 2021-02-09
Acknowledgements: This work was supported by National Science Foundation CAREER Electrical, Communications, and Cyber Systems grant 1454729 and by funding from King Abdullah University of Science and Technology. The authors thank Bassam Bamieh for helpful discussions.