An Adaptive Monte Carlo Test for Uncertain Discrete-Event Dynamic Systems

The analysis of uncertain dynamic discrete-event systems is generally intractable by deterministic numeric methods. In this paper, we propose an adaptive Monte Carlo test method to analyze systems. In contrast to the conventional methods of estimating the probability that a system fails to satisfy prespecified requirements, our goal is to determine whether the probability that the system violates the requirements. To accomplish this goal, we exploit a testing method based on the sequential probability ratio (SPRT) method invented by Wald. We demonstrate that such method can result in a substantial reduction of computational complexity as compared to conventional methods. To make the test method rigorous, we develop exact methods for computing the probability of making wrong decisions and the average number of simulations runs. The proposed method can be applied to investigate the stability of a control system with parametric uncertainty.