Data-Driven Approximate Abstraction for Black-Box Piecewise Affine Systems

How to effectively and reliably guarantee the correct functioning of safety-critical cyber-physical systems in uncertain conditions is a challenging problem. This paper presents a data-driven algorithm to derive approximate abstractions for piecewise affine systems with unknown dynamics. It advocates a significant shift from the current paradigm of abstraction, which starts from a model with known dynamics. Given a black-box system with unknown dynamics and a linear temporal logic specification, the proposed algorithm is able to obtain an abstraction of the system with an arbitrarily small error and a bounded probability. The algorithm consists of three components, system identification, system abstraction, and active sampling. The effectiveness of the algorithm is demonstrated by a case study with a soft robot.