Generalized Discrete Event Abstraction of Continuous Systems: Application to an Integrator

In this paper we present our recent work on generalized discrete event modelling. In the general framework of modelling and simulation of linear systems under time-continuous - or not - signals, the description of the integrator operator becomes fundamental as well as the description the time delay operator and the concept of output feedback. Therefore, this paper shall present the description of an integrator under piecewise linear input trajectories in a first step, then under trajectories described by a sequence of general order polynomials, ensuring a user given accuracy. Moreover, its remarkable behaviour in case of input discontinuities strongly contrast with the rather bad one of classical numerical solvers. Furthermore, a thorough comparison with discrete-time simulation techniques, like the classical Euler one, allows the assessment of an important computational gain using the techniques proposed here. Finally, the complete treatment of an hybrid system example not only illustrates the relevance of this approach, but underlines the interest of its application in the more general context of mixed-mode simulation and distributed simulation.[PUBLICATION ABSTRACT]