QSS method

The quantised state system (QSS) method introduced by Kofman [53] allows for a discrete event simulation of hybrid systems. The method starts from the observation that a piecewise constant trajectory can be represented by sequences of events. The reader is referred to the literature, e.g. references [1, 53, 54] for details. In the following, only the basic idea is outlined in a simplified manner. 

Let floor R Z+ denote a function that returns the integer part of its positive real-valued argument. The QSS-method then solves the approximate system... 

An attractive feature of a discrete event simulation of hybrid systems is that the simulation time advances from discrete event to discrete event. Eor the QSS method, discontinuities in the inputs and the quantised variables dictate the time advance. No iteration is necessary to locate the time point of a discontinuity allowing for an efficient processing of models with discontinuities. Discrete event simulation using the quantised-based integrations needs much less simulation steps than a numerical integration method of comparable accuracy based on time-discretisation. Accordingly, computational costs are saved. Nevertheless, there are still some problems to be tackled with the QSS approach as detailed in [1, Chap. 12.11]. 

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