My primary interests lie in the computational analysis of Cyber-Physical Systems, that involve the interaction of software components inside a physical system. Examples include software-based control systems for automotive, avionics and medical applications. The challenges include mathematical modeling of enviromental uncertainties, reasoning about these mathematical models to automatically prove or falsify correctness properties, and synthesizing core software subsystems automatically from given correctness specifications. My research addresses foundational (theoretical) issues including the theory of hybrid dynamical systems as well as applications to closed-loop medical devices and automotive systems.
I am part of the Programming Languages & Verification and Hybrid Systems communities, a very exciting area at the intersection of computer science and control theory. I take an active interest in topics that are directly relevant to my research, including convex optimization, randomized algorithms, algebraic/semi-algebraic geometry, combinatorial optimization, monte-carlo methods, symbolic and numerical decision procedures.