Compositional Construction of Finite MDPs for Large-Scale Stochastic Switched Systems: A Dissipativity Approach

Abstract

Abstract In this paper, we provide a compositional technique for constructing finite abstractions (a.k.a. finite Markov decision processes) for networks of discrete-time stochastic switched systems. The proposed framework is based on the notion of stochastic simulation functions, using which one can employ a finite MDP as a substitution of the original one in the controller design process with guaranteed error bounds on their output trajectories. In this respect, we first leverage dissipativity-type compositional conditions for quantifying the error between the interconnection of stochastic switched subsystems and that of their finite abstractions. We then propose an approach to construct finite MDPs together with their corresponding stochastic simulation functions for a particular class of nonlinear stochastic switched systems. To demonstrate the effectiveness of our proposed results, we apply our approaches to two different case studies.