Place: Seminar room - M2112B
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Formal methods from computer science were originally developed for specifying and verifying the correct behavior of software and hardware systems, and an important research objective now is to ensure these approaches are scalable, adaptable, and reliable when applied to physical control systems. Applying formal methods to such systems often requires computing finite state abstractions of the underlying dynamics. These finite abstractions over-approximate the original system so that any trajectory possible for the original system is also present in the finite abstraction.
Algorithms for computing finite abstractions usually require computing reachable sets as a fundamental subcomponent, which can be computationally prohibitive. In this talk, we will show that a large class of dynamical systems exhibit a mixed monotonicity property that generalizes the classical notion of monotone dynamical systems and allows for efficient computation of finite abstractions. In particular, mixed monotonicity enables reach set computations that scale linearly with the dimension of the continuous state space. We will also show that this approach extends to systems subject to stochastic disturbances, in which case the resulting finite-state abstraction can be interpreted as a Markov chain with uncertain transition probabilities. As an example, we apply the methodology to control of traffic flow networks, which are shown to be mixed monotone.
Sam Coogan is an assistant professor at Georgia Tech with a joint appointment in the School of Electrical and Computer Engineering and the School of Civil and Environmental Engineering. He currently holds the Demetrius T. Paris Junior Professorship in the School of ECE. Prior to joining Georgia Tech in July 2017, he was an assistant professor at UCLA from 2015-2017. He received the B.S. degree in Electrical Engineering from Georgia Tech and the M.S. and Ph.D. degrees in Electrical Engineering from the University of California, Berkeley. In 2015, he was a postdoctoral research engineer at Sensys Networks, Inc., and in 2012 he was a research intern at NASA's Jet Propulsion Lab. His research is in the area of dynamical systems and autonomy and focuses on developing scalable tools for verification and control of networked, cyber-physical systems with an emphasis on autonomous transportation systems. He received a Young Investigator Award from the Air Force Office of Scientific Research in 2018, a CAREER Award from the National Science Foundation in 2018, the IEEE Transactions on Control of Network Systems Outstanding Paper Award in 2017, and the best student paper award at the 2015 Hybrid Systems: Computation and Control conference.