Most critical infrastructures have evolved into complex systems comprising large numbers of interacting elements. These interactions result in the spread of disruptions, such as delays, from one part of the system to another, and even from one infrastructure to another. Effective tools for the analysis and control of real-world infrastructures need to account for the underlying dynamics. The key insight in this research is that by learning data-driven models of infrastructure networks, and using these models to determine dynamics-aware recovery algorithms, we can greatly improve the resilience of critical infrastructure networks. We propose to address these challenges by: 1. Learning and validating scalable representations of real systems from data. By considering continuous states, and by modeling the time-varying nature of connectivity as switching between network topologies, we propose to obtain a class of switched linear system models. Multilayer network models will be developed to account for airline networks, and multimodal systems. 2. Characterizing resilience, both for the system as a whole, and in terms of individual nodes (e.g., susceptibility to network delays). The metrics to evaluate resilience will encompass both steady-state and transient behavior. 3. Using the identified models to design optimal control algorithms that can enable recovery from disruptions, taking into account network dynamics, the uncertainty in operating environments, and the costs of decisions to restore service at various levels, at various times. The results of the research will be validated using operational data, thereby yielding a set of tools for system diagnostics, analysis, and recovery. Improving and maintaining critical infrastructures are among the grand challenges identified by the National Academy of Engineering. The proposed research will develop techniques grounded in network science, machine learning, and systems and control theory in order to effectively design and operate infrastructures. The development of common frameworks and abstractions for these infrastructures will enable the study of their interdependencies. With the rapid growth of intelligent infrastructures, the proposed research will benefit society, and also help attract and train the next generation of engineering professionals.