Generalized discrete event abstraction of continuous systems: GDEVS formalism

In this paper, we propose to model basic continuous component of dynamic systems in a way that facilitate the transposition to a G-DEVS model, which is a paradigm that offers the ability to develop a uniform approach to model hybrid systems (abstraction closer to real systems), i.e. composed of both continuous and discrete components. In that, our approach is clearly a discrete event approach where the choice of the time interval between two steps of calculation is based on the behavior changes of the process and no longer constant and/or a priori given, the underlying objective being to strictly satisfy to a given accuracy with a low computational cost. More precisely, we present a generalized discrete event model of an integrator using polynomial descriptions of input–output trajectories. We shall show its great capability of easily handling the delicate problem of input discontinuities, and a detailed comparison with classical discrete time simulation methods, will demonstrate its relevant properties. Several examples, including a complete hybrid system, will illustrate our results.