Séminaire en format hybride au GERAD local 4488 ou Zoom.

Stability and safety analysis of nonlinear dynamical systems has long been a central topic in control theory and dynamical systems research. Since Lyapunov’s landmark paper over a century ago, Lyapunov-like functions have become instrumental tools for analyzing nonlinear stability and safety, as well as for control design. Extensive research has focused on the construction of Lyapunov functions, a task that remains a significant challenge.

In this talk, we begin with a PDE-based formulation for constructing Lyapunov functions and demonstrate its interplay with physics-informed, data-driven techniques. We highlight how this integration can improve both solution quality and computational efficiency. Building on this foundation, we introduce a novel Zubov–Koopman operator-theoretic method for constructing maximal Lyapunov functions for unknown systems. This framework, exemplified by the speaker’s recent work, illustrates the benefits of combining physics-informed and learning-based approaches.

Finally, we present a research vision centered on a time-varying PDE-based formulation for constructing Lyapunov-barrier functions, aiming to address stability/reachability and safety verification – tasks that are often in conflict. Unifying Lyapunov and barrier functions is nontrivial, and the approach that builds on recent advances in Zubov–Koopman operator-theoretic verification shows promise in estimating the maximal region where these specifications can be satisfied. This region coincides with the largest domain in which Lyapunov and barrier functions can be coherently unified.