The theme of this project is control of hybrid systems based on limited (sampled and quantized) information about their state. The project aims to bring together, for the first time, two research topics: hybrid systems, and control with limited information. The project will seek to develop a novel method for propagating over-approximations of reachable sets for hybrid systems, and use it to define and validate a control strategy based on sampled and quantized measurements of the continuous state. This method will be combined with state-of-the-art analysis tools for hybrid and switched systems, such as multiple Lyapunov functions, average dwell-time switching, and input-to-state stability.
Hybrid systems are important for modeling and controlling the behavior of cyber-physical systems, such as fly-by-wire aircraft and power grids. Hybrid systems combine continuous dynamics and discrete transitions. This hybrid nature enables one to capture many processes encountered in practice which switch between different modes of operation. Controllers for such systems typically have limited information about the system state, due to limitations of available sensors and delays and losses in communication. A possible scenario is controlling an autonomous robot which switches between the search mode and the pursuit mode and, for security or implementation cost reasons, is connected to the control center via a very low-power communication link. Educational and outreach activities of the project include support of a graduate student, integration of the research with graduate courses in hybrid systems and control, workshops and short courses, and involvement of undergraduates in translating theoretical developments into software tools.
