Compositional approximations of interconnected stochastic hybrid systems

This paper provides a compositional approach for approximations of the interconnection of a class of stochastic hybrid systems including both jump linear stochastic systems and linear stochastic hybrid automata. The approximation is based on the recently developed notions of stochastic (bi)simulation functions using which one can quantify the error between original stochastic hybrid systems and their abstractions. Given stochastic (bi)simulation functions between stochastic hybrid subsystems and their corresponding approximations, we provide a stochastic (bi)simulation function between an interconnection of those stochastic hybrid subsystems and that of their corresponding approximations. Consequently, one can leverage the proposed results in this paper to perform the analysis and synthesis over the interconnection of abstract subsystems and then carry the results over the interconnection of concrete ones. We illustrate the effectiveness of the proposed results here by computing a stochastic (bi)simulation function between an interconnection of two identical jump linear stochastic subsystems and that of their corresponding approximations by just using the stochastic (bi)simulation function between one of the jump linear stochastic subsystems and its corresponding approximate abstraction.