Further results on probabilistic model validation in Wasserstein metric

In a recent work [1], we have introduced a probabilistic formulation for the model validation problem to provide a unifying framework for (in)validating nonlinear deterministic and stochastic models, in both discrete and continuous time. As an extension to that work, this paper provides rigorous performance bounds for the model validation algorithms presented in [1]. Further, it is shown that the existing method of barrier certificate based nonlinear invalidation oracle, can be recovered as a special case of the proposed formulation. Some results are derived to quantify the effects of initial uncertainty on the Wasserstein gap. And finally, for discrete-time LTI and LTV systems, upper bounds on Wasserstein distance are derived in terms of the parameters of the systems under comparison, thus providing an offline estimate of the gap.