Abstract: Reachability analysis is the problem of computing attainable states of a system while accounting for disturbances from the environment and uncertainties in the model. This fundamental problem has diverse applications in safety verification, controller synthesis, and estimation. It is known that even for small-sized systems, exact reachability analysis is notoriously difficult. This challenge escalates significantly when dealing with large-sized systems or incorporating large-scale learning-based components. In this talk, we use monotone system theory to develop a computationally efficient framework for approximating the reachable sets of large-scale control systems. In particular, our framework provides a rigorous method to obtain over-approximation of reachable sets and to search for invariant sets of control systems. We also study the reachability of control systems with learning-based components in the loop. We demonstrate how our framework can be efficiently integrated with existing verification approaches for learning algorithms to correctly capture the interaction between the learning-based component and the rest of the system.

Bio: Saber is currently a Research Associate and a Lecturer in the Department of Electrical, Computer, and Energy Engineering. Before joining CU Boulder, he was a Postdoctoral Research Fellow in the Decision and Control Laboratory at the Georgia Institute of Technology working with Sam Coogan and a Postdoctoral Research Fellow with the Center for Control, Dynamical Systems, and Computation at the University of California, Santa Barbara, working with Francesco Bullo. Saber did his PhD in the Department of Mathematics and Statistics at Queen's University under supervision of Andrew Lewis.

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