28 citations · 61 across the 15 of their papers we have counts for
4 papers · 1 filter
A Converse Control Lyapunov Theorem for Joint Safety and Stability
Thanin Quartz, Maxwell Fitzsimmons, Jun Liu
We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that…
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE…
Towards Learning and Verifying Maximal Neural Lyapunov Functions
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
The search for Lyapunov functions is a crucial task in the analysis of nonlinear systems. In this paper, we present a physics-informed neural network (PINN) approach to learning a…
A Necessary Condition on Chain Reachable Robustness of Dynamical Systems
Maxwell Fitzsimmons, Jun Liu
It is ``folklore'' that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can b…