Numerically-Robust Inductive Proof Rules for Continuous Dynamical Systems
Sicun Gao, James P. Kapinski, Jyotirmoy V. Deshmukh, Nima Roohi, Armando Solar-Lezama, Nikos Aréchiga, Soonho Kong · Lecture notes in computer science · 2019
We formulate numerically-robust inductive proof rules for unbounded stability and safety properties of continuous dynamical systems. These induction rules robustify standard notions of Lyapunov functions and barrier certificates so that they can tolerate small numerical errors. In this way, numerically-driven decision procedures can establish a sound and relative-complete proof system for unbounded properties of very general nonlinear systems. We demonstrate the effectiveness of the proposed rules for rigorously verifying unbounded properties of various nonlinear systems, including a challenging powertrain control model.