Stochastic hybrid systems

Hybrid systems are a powerful modeling framework able to capture the intricacy of complex systems arising in a variety of domains. In the hybrid systems literature, uncertainty affecting the system evolution is often modeled through non-determinism; roughly speaking, this implies that all executions are equally likely. In stochastic hybrid systems, uncertainty is instead modeled by introducing probabilistic components in the system evolution, and executions are stochastic processes on a hybrid state space. As a result, stochastic hybrid systems are more expressive and offer a larger variety of problems with different nuances to study. Starting from these observations, we introduce stochastic hybrid automata as the probabilistic version of (non-deterministic) hybrid automata and provide a summary of the modeling capabilities of different classes of continuous time stochastic hybrid systems in the literature. Finally, we introduce a discrete time version of stochastic hybrid automata with same qualitative modeling features of its continuous time counterpart.