Approximate Abstraction of Stochastic Hybrid Automata

This paper discusses a notion of approximate abstraction for linear stochastic hybrid automata (LSHA). The idea is based on the construction of the so called stochastic bisimulation function. Such function can be used to quantify the distance between a system and its approximate abstraction. The work in this paper generalizes our earlier work for jump linear stochastic systems (JLSS). In this paper we demonstrate that linear stochastic hybrid automata can be cast as a modified JLSS and modify the procedure for constructing the stochastic bisimulation function accordingly. The construction of quadratic stochastic bisimulation functions is essentially a linear matrix inequality problem. In this paper, we also discuss possible extensions of the framework to handle nonlinear dynamics and variable rate Poisson processes. As an example, we apply the framework to a chain-like stochastic hybrid automaton.