Hybrid systems model dynamic behavior that combines continuous evolution and instantaneous change. A wide class of naturally occurring and engineered systems exhibit hybrid dynamics. Examples include air traffic management systems, impulsively coupled biological oscillators, and networked and logic-based control systems. Over the last decade, significant progress has been made on characterizing worst-case, robust asymptotic stability in hybrid dynamical systems. General invariance principles, converse Lyapunov theorems, reduction principles, and linearization-based results have been established. Worst-case refers to the fact that these results pertain to hybrid systems that may admit non-unique solutions, a situation that is common in hybrid systems modeling. The aim of the current proposal is to extend these recent insights about worst-case asymptotic stability in hybrid systems to the stochastic setting. We propose to develop a robust, asymptotic stability theory for hybrid systems that feature some effects of a worst-case nature and some effects that are stochastic, a common occurrence in many naturally occurring and engineered hybrid systems, including networked control systems, air traffic management systems, biological systems, and financial systems. The proposed contributions to stability theory for stochastic hybrid systems will help pave the way for advances in control design for stochastic hybrid systems.
Broader impact:
The proposed effort will contribute to the engineering education base by furthering the available graduate curriculum on hybrid systems, and by training graduate students in UCSB?s Center for Control, Dynamical Systems, and Computation. Tutorial workshops at the main control conferences will be delivered to interested graduate students, faculty, and industry personnel. All work will be documented in acclaimed international conferences and prestigious control and dynamical systems journals. Collaboration with international researchers will be fostered, including student exchange programs, most notably with the University of Melbourne, and the University of Rome, Tor Vergata. The theoretical results of the proposed work will be applied to areas that are significant to the broad population, including problems like the efficient management of air traffic to enhance throughput in the nation?s aviation system. Most notably, we will continue our work with UCSB?s summer internship program aimed at undergraduate students, which has led to recent successful mentoring experiences for our control graduate students who have supervised undergraduate students from various underrepresented student populations.
