Active Sampling-Based Binary Verification of Dynamical Systems

Abstract

© 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While ana- lytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system’s response at different operating conditions, they often produce con- servative approximations due to restrictive assumptions and are dificult to construct in many applications. In contrast, popular statistical verification techniques relax the restric- tions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into “safe” and “unsafe” subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction er- ror. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.