Probabilistic Reachability Analysis for Large Scale Stochastic Hybrid Systems

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

Sequential Monte Carlo simulation for the estimation of small reachability probabilities for stochastic hybrid systems

The problem of estimating the probability that a system reaches a given set within some time horizon is considered. Standard Monte Carlo methods for reachability probability estimation do not require specific assumptions on the system under consideration. However, they are computationally demanding when the probability to be estimated is small. An Interacting Particle System (IPS) approach has been developed for the estimation of small reachability probabilities for diffusion processes. IPS has then been extended so as to estimate small reachability probabilities for a certain family of stochastic hybrid processes, namely switching diffusions. This contribution further improves the hybrid IPS method by adopting an importance sampling approach that uses the interaction equations characterizing stochastic hybrid systems