Performance assessment and design of abstracted models for stochastic hybrid systems through a randomized approach

In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the realizations of the stochastic input except for a set of (small) probability ε (ε-abstraction). This naturally leads to chance-constrained optimization problems, which are here tackled by means of a recently developed randomized approach. The main thrust of this paper is that, by testing how close the model and system outputs are over a finite number N of input realizations only, conclusions can be drawn about the model capability as an ε-abstraction. The key feature of the proposed method is its high versatility since it does not require specific assumptions on the system to be approximated. The only requirement is that of being able to run multiple simulations of the system behavior for different input realizations.