Mathematics Colloquia and Seminars

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Hybrid systems are a suitable model for representing systems that can transition between different behaviors. Many engineered systems are designed to be hybrid in order to simplify function and maintain flexibility in operation. For example, air traffic control systems involve transitions between simple flight modes for multiple aircraft. Hybrid systems are also a good framework for modeling natural systems: in cell biology, the dynamics that govern the spatial and temporal increase or decrease of protein concentration inside a single cell are continuous differential equations derived from biochemistry, yet their activation or deactivation is triggered by transitions which encode protein concentrations reaching given thresholds. In this talk, methods that have been designed to analyze, verify, and control hybrid systems will be presented. The methods use tools from game theory, wavefront propagation, and symbolic predicate abstraction, and rely on an iterative refinement procedure which computes, either exactly or approximately, regions of the system's operating space in which desired behavior is guaranteed. I will focus on two large scale examples: the design and implementation of real time collision avoidance schemes for manned and unmanned air vehicles, and the development of models of cellular regulatory networks in developmental biology. Joint work with Ian Mitchell, Alex Bayen, Ronojoy Ghosh, Meeko Oishi, Jeff Axelrod, and Keith Amonlirdviman.

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