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

TL;DR

This paper introduces a data-driven approach for model invalidation of unknown Lipschitz continuous systems using noisy sampled data, combining abstraction and optimization to verify system compatibility with observed trajectories.

Contribution

It proposes a novel tractable method that over-approximates unknown system dynamics from data and checks model validity without explicit mathematical models.

Findings

Effective in invalidating models with noisy data

Reduces computational complexity through specific methods

Demonstrated success in swarm intent identification simulation

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.