2024-2025 Seminar Series
Upcoming Seminar
Speaker: Sylvia Herbert (University of California, San Diego)
Title: Scalable safety analysis and control synthesis for nonlinear differential games
Abstract: Hamilton-Jacobi (HJ) Reachability analysis is a powerful tool for solving differential games with bounded inputs; it can provide safety and liveness guarantees for each player and the corresponding optimal control law. However, control theoretic approaches to solving nonlinear differential games struggle with the "curse of dimensionality." We will explore two methods for overcoming this issue, one with conservative guarantees and one with probabilistic guarantees.
Recently, the applied math community has been exploring the use of the Hopf formula for efficiently solving linear differential games with bounded inputs via ADMM. We will show how we can lift a nonlinear game to a linear space wherein we can bound linearization error. We can then treat this error as an adversary in a linear game solvable by the Hopf formula, with results that can map back to the original space for conservative guarantees on the true nonlinear game. More recently, solving HJ reachability using model-based supervised learning via physics-informed neural networks (PINNs) has become increasingly popular because the computation time scales with complexity rather than dimensionality. However, these PINNs suffer from learning errors and catastrophic forgetting. We will show how linear supervision (e.g. from the same Hopf formula above) of the nonlinear game can significantly improve the learning results, resulting in tighter probabilistic guarantees. This work was recently nominated for the Best Paper Award at the Learning for Dynamics and Control (L4DC) conference.
Date: Thursday, April 3rd, 2025
Time: 10:00-11:00 AM EDT
Link: https://columbiauniversity.zoom.us/j/91247893326?pwd=L2JWU21aQzc4cU1ZQklEb0QrWGQvdz09
Line-Up and Video Links
| Date | Speaker | Title | YouTube |
|---|---|---|---|
| Dec. 5, 2024 | Andrea Del Prete | Globally Optimal and Safe Robot Control | (link) |
| Feb. 6, 2025 | Ian Abraham | Optimality and Robustness in Robotic Exploration | (link) |
| Feb. 21, 2025 | Cosimo Della Santina | Motor intelligence in soft robots and other unconventional robotic systems | (link) |
| Mar. 13, 2025 | Jemin Hwangbo | Learning-based control for quadrupedal robots | [(to be uploaded)] |
| Apr. 3, 2025 | Sylvia Herbert | Scalable safety analysis and control synthesis for nonlinear differential games |