My research lies at the intersection of optimization and control, two fields that play a vitally important role in cyber-physical systems (CPS) applications but that tend to have very different goals and tools. My research thrust is to leverage the strengths of both fields with the ultimate goal of enabling safe and efficient complex systems. I have participated in several projects that build toward this goal, and brief summaries are provided below. Click on each item for an expanded description. [more]

Optimization as robust control
(with B. Recht, A. Packard, and others)

The problem of selecting a suitable algorithm for use in large-scale optimization is currently more of an art than a science. In this work, we show that algorithm selection (and design!) can be cast as a robust control problem. This work unifies many existing results in optimization theory and provides a principled way to analyze or design algorithms based on practical characteristics such as robustness to noise. [more]

Safety validation for interconnected systems
(with C. Meissen, M. Arcak, and A. Packard)

Many control techniques exist for certifying the safety or performance of a well-modeled system, but these techniques become computationally intractable if the system is anything but modest in size. Large systems are often, however, built by interconnecting smaller subsystems. We developed a scalable distributed optimization methodology that can efficiently certify such interconnected systems. [more]

Control under information constraints
(with S. Lall, A. Nayyar, and A. Lamperski)

A defining characteristic of large-scale systems is that control decisions must be made in multiple parts of the system, but the decision-makers have access to different information. This could be due to delays in the network or other communication constraints. In this work, we found that certain classes of information-sharing architectures lead to tractable control problems, and we can often solve them explicitly. [more]

Control of ground-based telescopes
(with: D. MacMynowski, M. West, S. Lall, and others)

Large ground-based telescopes use adaptive optics (AO) technology to mitigate atmospheric distortion. This works surprisingly well but requires 100s or 1000s of sensors and individually actuated mirrors. AO control is computationally demanding and does not scale well to future larger telescopes. We designed algorithms for AO that scale much better than conventional techniques without compromising image quality. [more]