Case Studies in Data-Driven Verification of Dynamical Systems

We interpret several dynamical system verification questions, e.g., region of attraction and reachability analyses, as data classification problems. We discuss some of the tradeoffs between conventional optimization-based certificate constructions with certainty in the outcomes and this new date-driven approach with quantified confidence in the outcomes. The new methodology is aligned with emerging computing paradigms and has the potential to extend systematic verification to systems that do not necessarily admit closed-form models from certain specialized families. We demonstrate its effectiveness on a collection of both conventional and unconventional case studies including model reference adaptive control systems, nonlinear aircraft models, and reinforcement learning problems.