My work spans across the topics of control, dynamics, computation, optimization, and networks. Almost all of my work is done in collaboration with researchers from application areas. Challenges in real-world problems motivate development of new theory. This theory implies a strategy and methodology for solving these problems computationally. Insights from computation provide advancements in the application as well as suggest new approaches for the theory. And so the cycle continues.
Networks have become a popular and effective way of modeling the structure and function of a large variety of complex systems – from the infrastructure for telecommunication systems, to interconnections between neurons, to interactions via social media. Very little work has been done on understanding the properties of these systems from a control theoretic point-of-view. Our work lays down the foundation of how to begin to look at this very challenging new area of research.
Security of Cyber-Physical Systems
To a large degree, control engineering is a “hidden” technology, in the sense that it permits the efficient operation of everything from the hard-disks in our computers, to cruise-control in our cars, to regulation in refineries and power plants. Many of these applications are in some of our most critical infrastructures – e.g., power, water, transportation. Control theory has a long history of designing systems to be able to operate in the presence of undesirable noise and model uncertainty. Security of control systems, however, presents all new challenges to the control community. Assumptions that have been made – for example for the Kalman Filter – are no longer valid as soon as perturbations to the system may have been caused by an adversarial attacker rather than random failure. The systematic and persistent nature of attacks identifies key vulnerabilities of control systems. Our work uses the coupling of the physical layer to detect attacks by quantifying the analytic relationships between detection method parameters (e.g., thresholds), the largest undetected deviation of the state possible, and the expected rate of false alarms.
In this work, we develop a new framework and novel methods to synthesize optimal, open-loop controls for a class of complex dynamical systems called inhomogeneous ensembles. Such systems are motivated by the challenges arising from pulse design problems in nuclear magnetic resonance (NMR) and imaging (MRI), but also appear in additional areas of quantum control as well as in uncertain systems across science and engineering.
Computational Optimal Control
Many disciplines and applications have yet to incorporate the systematic approaches that control theory offers into the way that they operate and understand their problems. Our work in computation optimal control attempts to take the siloed tools from dynamical systems and optimal control and apply them on a wide range of problems. We have used this approach in a variety of applications including: control of quantum systems, neuroscience, and human eye and head dynamics.