Discrete abstraction for a class of stochastic hybrid systems based on bounded bisimulation

Stochastic hybrid systems can express complex dynamical systems such as biological systems and communication networks, but computation for analysis and control is frequently difficult. In this paper, for a class of stochastic hybrid systems, a discrete abstraction method in which a given system is transformed into a finite-state system is proposed based on the notion of bounded bisimulation. In the existing discrete abstraction method based on bisimulation, a computational procedure is not in general terminated. In the proposed method, only the behavior for the finite time interval is expressed as a finite-state system, and termination is guaranteed. The obtained discrete abstract model can be used for model predictive control in which the finite-time optimal control problem is solved at each time. Furthermore, as an application, analysis of genetic toggle switches is also discussed.