Data-Driven Model Invalidation for Unknown Lipschitz Continuous Systems via Abstraction

Abstract

In this paper, we consider the data-driven model invalidation problem for Lipschitz continuous systems, where instead of given mathematical models, only prior noisy sampled data of the systems are available. We show that this data-driven model invalidation problem can be solved using a tractable feasibility check. Our proposed approach consists of two main components: (i) a data-driven abstraction part that uses the noisy sampled data to over-approximate the unknown Lipschitz continuous dynamics with upper and lower functions, and (ii) an optimization-based model invalidation component that determines the incompatibility of the data-driven abstraction with a newly observed length-T output trajectory. Finally, we discuss several methods to reduce the computational complexity of the algorithm and demonstrate their effectiveness with a simulation example of swarm intent identification.