Probabilistic reachability analysis for large scale stochastic hybrid systems

Abstract

Abstract-This paper studies probabilistic reachability analysis for large scale stochastic hybrid systems (SHS) as a problem of rare event estimation. In literature, advanced rare event estimation theory has recently been embedded within a stochastic analysis framework, and this has led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This paper presents this rare event estimation theory directly in terms of probabilistic reachability analysis of an SHS, and develops novel theory which allows to extend the novel results for application to a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the reach probability. Essentially, the approach taken is to introduce an aggregation of the discrete modes, and to develop importance sampling relative to the rare switching between the aggregation modes. The practical working of this approach is demonstrated for the safety verification of an advanced air traffic control example.

Large deviation methods for stochastic reachability

“…The relevance of large deviation methods for stochastic reachability should not be judged in the context of simulation approaches for stochastic reachability. Rare event simulation methods (like importance sampling, importance splitting) SHS are treated by different other papers as [3]. We have provided large deviation methods for different measures (exit probabilities, occupation time distributions) associated to the stochastic reachability problem.…”

Reachability Analysis of Stochastic Hybrid Systems: A Biodiesel Production System

“…The analysis of these ensemble properties can significantly improve the understanding of the entire system [7]. Variance reduction methods based on importance sampling have been developed for Monte Carlo methods with rare events [31,11], but tuning the methods for high dimensional systems is difficult and can actually reduce the performance of the estimator [23].…”

Stochastic hybrid models for predicting the behavior of drivers facing the yellow-light-dilemma

“…Stochastic reachability problems have been studied in the stochastic hybrid systems literature, see [16], [17], [18], [19]. Exact computation of reach probabilities remains a challenging problem but Monte Carlo methods have proven to be an efficient way to deal with the complexity of stochastic hybrid systems, see [17].…”

“…Exact computation of reach probabilities remains a challenging problem but Monte Carlo methods have proven to be an efficient way to deal with the complexity of stochastic hybrid systems, see [17].…”