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Compositional finite abstractions for large-scale stochastic switched systems

In this paper, we provide for the first time a compositional methodology for the construction of finite MDPs for networks of stochastic switched systems. The proposed technique leverages sufficient small-gain type conditions to establish the compositionality results which rely on relations between subsystems and their abstractions described by the existence of stochastic simulation functions. This type of relations enable us to compute the probabilistic error between the interconnection of concrete subsystems and that of their finite abstractions. In this respect, we show that if a switched system is incremental input-to-state stable (i.e., existence of a common incremental Lyapunov function, or multiple incremental Lyapunov functions with dwell-time), one can construct stochastic simulation functions between finite abstractions and concrete models. We also propose a construction framework for a particular class of nonlinear stochastic switched systems by satisfying some easier to check matrix inequalities. To demonstrate the effectiveness of our proposed results, we apply our approaches to two different case studies.