Hans Vangheluwe

Cláudio Gomes, Casper Thule, David Broman et al.

It is essential to find new ways of enabling experts in different disciplines to collaborate more efficient in the development of ever more complex systems, under increasing market pressures. One possible solution for this challenge is to use a heterogeneous model-based approach where different teams can produce their conventional models and carry out their usual mono-disciplinary analysis, but in addition, the different models can be coupled for simulation (co-simulation), allowing the study of the global behavior of the system. Due to its potential, co-simulation is being studied in many different disciplines but with limited sharing of findings. Our aim with this work is to summarize, bridge, and enhance future research in this multidisciplinary area. We provide an overview of co-simulation approaches, research challenges, and research opportunities, together with a detailed taxonomy with different aspects of the state of the art of co-simulation and classification for the past five years. The main research needs identified are: finding generic approaches for modular, stable and accurate coupling of simulation units; and expressing the adaptations required to ensure that the coupling is correct.

Cláudio Gomes, Yentl Van Tendeloo, Joachim Denil et al.

For a wide variety of problems, creating detailed continuous models of (continuous) physical systems is, at the very least, impractical. Hybrid models can abstract away short transient behaviour (thus introducing discontinuities) in order to simplify the study of such systems. For example, when modelling a bouncing ball, the bounce can be abstracted as a discontinuous change of the velocity, instead of resorting to the physics of the ball (de-)compression to keep the velocity signal continuous. Impulsive differential equations can be used to model and simulate hybrid systems such as the bouncing ball. In this approach, the force acted on the ball by the floor is abstracted as an infinitely large function in an infinitely small interval of time, that is, an impulse. Current simulators cannot handle such approximations well due to the limitations of machine precision. In this paper, we explore the simulation of impulsive differential equations, where impulses are first class citizens. We present two approaches for the simulation of impulses: symbolic and numerical. Our contribution is a theoretically founded description of the implementation of both approaches in a Causal Block Diagram modelling and simulation tool. Furthermore, we investigate the conditions for which one approach is better than the other.

Cláudio Gomes, Raphaël M. Jungers, Benoît Legat et al.

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.

Yentl Van Tendeloo, Hans Vangheluwe

DEVS is a popular formalism to model system behaviour using a discrete-event abstraction. The main advantages of DEVS are its rigourous and precise specification, as well as its support for modular, hierarchical construction of models. DEVS frequently serves as a simulation "assembly language" to which models in other formalisms are translated, either giving meaning to new (domain-specific) languages, or reproducing semantics of existing languages. Despite this rigourous definition of its syntax and semantics, initialization of DEVS models is left unspecified in both the Classic and Parallel DEVS formalism definition. In this paper, we extend the DEVS formalism by including an initial total state. Extensions to syntax as well as denotational (closure under coupling) and operational semantics (abstract simulator) are presented. The extension is applicable to both main variants of the DEVS formalism. Our extension is such that it adds to, but does not alter the original specification. All changes are illustrated by means of a traffic light example.

Jonathan Sprinkle, Bernhard Rumpe, Hans Vangheluwe et al.

This chapter discusses the current state of the art, and emerging research challenges, for metamodelling. In the state-of-the-art review on metamodelling, we review approaches, abstractions, and tools for metamodelling, evaluate them with respect to their expressivity, investigate what role(s) metamodels may play at run-time and how semantics can be assigned to metamodels and the domain specific modeling languages they could define. In the emerging challenges section on metamodelling we highlight research issues regarding the management of complexity, consistency, and evolution of metamodels, and how the semantics of metamodels impacts each of these.