Automated verification and synthesis of stochastic hybrid systems: A survey

Stochastic hybrid systems have received significant attentions as a relevant modeling framework describing many systems, from engineering to the life sciences: they enable study of numerous applications, including transportation networks, biological and chemical reaction smart energy power grids, beyond. Automated verification policy synthesis for stochastic can be inherently challenging: this is due heterogeneity their dynamics (presence continuous discrete components), presence uncertainty, in some applications large dimension state input sets. Over past few years, hundred articles investigated these models, developed diverse powerful approaches mitigate difficulties encountered analysis such complex systems. In survey, we overview most recent results literature discuss different approaches, (in)finite abstractions, temporal logic specifications, similarity relations, (control) barrier certificates, compositional techniques, selection on continuous-time systems; finally survey recently software tools that implement discussed approaches. Throughout manuscript open topics considered potential future research directions: hope will guide younger researchers through comprehensive understanding various challenges, tools, solutions enticing rich scientific area.