Seminar Details
2024-03-26 (14h) : Safety of stochastic systems: from stochastic barrier functions to uncertain abstractions
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Luca Laurenti (TU Delft)
Abstract :
Providing safety guarantees for stochastic dynamical systems has become a central problem in many fields, including control theory, machine learning, and robotics. In this talk I will present our recent work on providing safety guarantees for non-linear stochastic dynamical systems, including dynamical systems with neural networks in the loop. I will focus on two different approaches to quantify safety for stochastic systems: Stochastic Barrier Functions (SBFs) and abstractions to uncertain Markov models. While SBFs are analogous to Lyapunov functions to prove (probabilistic) set invariance, abstraction-based approaches approximate the stochastic system into a finite model for the computation of safety probability bounds. I will illustrate pros and cons both methods. I will then conclude the talk illustrating how recent results from optimal transport and stochastic approximation could be employed to complement both methods to finally provide scalable safety guarantees for non-linear uncertain systems.