Data-Driven Abstraction and Model Invalidation for Unknown Systems With Bounded Jacobians

In this letter, we consider data-driven abstraction and model invalidation problems for unknown nonlinear discrete-time dynamical systems with bounded Jacobians, where only prior noisy sampled data of the systems, instead of mathematical models, are available. First, we introduce a novel non-parametric learning approach to over-approximate the unknown model/dynamics with upper and lower functions, i.e., to find model abstractions, under the assumption of known bounded Jacobians. Notably, the resulting data-driven models can be mathematically proven to be equal to or more accurate than componentwise Lipschitz continuity-based methods. Further, we show that the resulting data-driven model can be used to determine its (in)compatibility with a newly observed length-$T$ output trajectory, i.e., to (in)validate models, using a tractable feasible check. Finally, we propose a method to estimate the Jacobian bounds if they are not known or given.