My primary research interest is the modeling, analysis, and control of dynamical processes and strategic interactions in complex interconnected systems, with applications in social networks, electric power distribution, robotic networks, and biological systems. Since critical societal functions are increasingly dependent on these complex networks, it is important to ensure that their performance and reliability are not degraded as the structure of the network evolves over time. This requires us to acquire a deeper understanding of the relationship between the structure and dynamics of these complex systems.
Understanding the dynamics of complex networks is a challenging problem due to:
- The cumbersome size and complexity of the systems (e.g. the Internet),
- The nonexistence of a vantage point with complete information about the structure of the system (e.g. social networks), and
- The structure of the system itself may be changing over time (e.g. microgrids, where supply and demand of electricity are intermittent).
My current research is devoted to building a rigorous theoretical foundation to analyze massive networks of dynamical elements using tools and techniques at the intersection of dynamical systems, control theory, probability, optimization, and graph theory. Alongside, I use real experimental data from technological networks (e.g. electric transmission networks and the Internet), as well as online social networks (e.g. Facebook and Twitter graphs) to validate theoretical predictions and build computational tools of practical interest.
- Cassiano Becker (Ph.D candidate)
- Ximing Chen (Ph.D candidate)
- Mahyar Fazlyab (Ph.D candidate)
- David Sun (Ph.D candidate)
- Ishaan Nerurkar