Prevalence and scalable control of localized networks

Abstract

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks as well as three large empirical networks: synchronization dynamics in the Eastern U.S. power grid, epidemic spreading mediated by the global air transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

arXiv commentCodes are available on GitHub (https://github.com/cduan2020/LocalizedControl/)

References in corpus (24)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Community structure in social and biological networks
• Synchronization in complex networks
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Synchronization in Complex Oscillator Networks and Smart Grids
• Spontaneous synchrony in power-grid networks
• Control Principles of Complex Networks
• On Submodularity and Controllability in Complex Dynamical Networks
• Controlling complex networks: How much energy is needed?
• Realistic Control of Network Dynamics
• Spectrum of Controlling and Observing Complex Networks
• Structure-based control of complex networks with nonlinear dynamics
• Controllability transition and nonlocality in network control
• Observability and Controllability of Nonlinear Networks: The Role of Symmetry
• Moment Closure - A Brief Review
• Rescuing ecosystems from extinction cascades through compensatory perturbations
• Control of coupled oscillator networks with application to microgrid technologies
• Energy Scaling of Targeted Optimal Control of Complex Networks
• Networkcontrology
• Time-evolving controllability of effective connectivity networks during seizure progression
• On Structural Controllability of Symmetric (Brain) Networks
• Functional observability and target state estimation in large-scale networks
• Non-Fragility and Partial Controllability of Multi-Agent Systems

Cited by in corpus (5)

• Target Controllability and Target Observability of Structured Network Systems
• Dynamical heterogeneity and universality of power-grids
• Low-dimensional controllability of brain networks
• Global network control from local information
• Designing topological cluster synchronization patterns with the Dirac operator