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Explore a GERAD Research Center seminar where Yiming Meng from the University of Illinois at Urbana-Champaign discusses innovative approaches to stability and safety analysis for unknown nonlinear systems. Discover how PDE-based formulations for constructing Lyapunov functions can be integrated with physics-informed, data-driven techniques to enhance solution quality and computational efficiency. Learn about a novel Zubov–Koopman operator-theoretic method for constructing maximal Lyapunov functions when working with unknown systems. Examine the research vision for a time-varying PDE-based approach to constructing Lyapunov-barrier functions that addresses the often conflicting tasks of stability/reachability and safety verification. Understand how recent advances in Zubov–Koopman operator-theoretic verification can help estimate the maximal region where stability and safety specifications can be simultaneously satisfied, representing the largest domain where Lyapunov and barrier functions can be coherently unified.
