Research Interests

Hybrid Control Systems: These are systems which combine continuous time dynamics with discrete event dynamics. Research involves design, verification using new computational methods for computing reachable sets, and simulation of hybrid systems. We are currently developing the theory and designing models to predict the behavior of complex systems.
This work is supported by NSF, ONR, and AFOSR.

Air Traffic Control Automation: This is joint work with NASA Ames to design models of and control systems for Air Traffic dynamics. This research includes algorithms for automatic resolution of trajectory conflicts between multiple aircraft, as well as novel polynomial time scheduling algorithms.

Algorithms for Decentralized Optimization: In this project, we are designing algorithms with provable convergence properties for decentralized optimization — meaning that several interconnected units act as local decision-makers and optimize local costs, coordinating with each other through constraints. This work is supported by NSF, ONR, and AFOSR.

Human-automation Systems: This research involves analysis of systems for which the control authority is shared between human and automation. We work on the analysis of autopilot systems, driving systems, and robotic systems.

Modeling and Analysis of Biological Cell Networks: In this research project we are building models and analysis tools for helping to understand biological cell networks. Current research includes HER2+ breast cancer, early stage Drosophila development, and planar cell polarity in Drosophila. This is joint work with OHSU, LBNL, UCSF, and Stanford, and is supported by grants from the NCI and NIH.

Unmanned Aerial Vehicle Design and Control: In this project we are building a team of UAVs with the goals of studying formation flying, architectures for distributed control, and methods for reliable control over communication links.

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