Non-standard semantics of hybrid systems modelers

Abstract:

Hybrid system modelers have become a corner stone of complex embedded system development. Embedded systems include not only control components and software, but also physical devices. In this area, Simulink is a de facto standard design framework, and Modelica a new player. However, such tools raise several issues related to the lack of reproducibility of simulations (sensitivity to simulation parameters and to the choice of a simulation engine). In this paper we propose using techniques from non-standard analysis to define a semantic domain for hybrid systems. Non-standard analysis is an extension of classical analysis in which infinitesimal (the ε and η in the celebrated generic sentence ∀ε∃η… of college maths) can be manipulated as first class citizens. This approach allows us to define both a denotational semantics, a constructive semantics, and a Kahn Process Network semantics for hybrid systems, thus establishing simulation engines on a sound but flexible mathematical foundation. These semantics offer a clear distinction between the concerns of the numerical analyst (solving differential equations) and those of the computer scientist (generating execution schemes). We also discuss a number of practical and fundamental issues in hybrid system modelers that give rise to non-reproducibility of results, non-determinism, and undesirable side effects. Of particular importance are cascaded mode changes (also called “zero-crossings” in the context of hybrid systems modelers).

Presentation Slides

Biography:

Albert Benveniste was born in 1949. He graduated in 1971 from Ecole des Mines de Paris. He performed his These d'Etat in Mathematics, probability theory, in 1975, under the supervision of Paul-André Meyer. From 1976 to 1979 he was associate professor in mathematics at Universite de Rennes I. From 1979 to now he has been Directeur de Recherche at INRIA.

In 1980 Albert Benveniste was co-winner of the IEEE Trans. on Automatic Control Best Transaction Paper Award for his paper on blind deconvolution in data communications. In 1990 he received the CNRS silver medal and in 1991 he has been elected IEEE fellow. In 2008 he was winner of the Grand Prix France Telecom of the french Academy of Sciences. From 1986 to 1990 he was vice-chairman of the IFAC committee on Theory and was chairman of this committee for 1991-1993. He has been or is Associate Editor (at Large) for IEEE Transactions on Automatic Control, Associate Editor for Int. J. of Adaptive Control and Signal Processing, and Int. J. of Discrete Event Dynamical Systems. He is currently member of the Editorial Board of the Proceedings of the IEEE. From 1994 to 1996 he has been Directeur Scientifique (Senior Chief Scientist) at Inria. From 1997 to 2001, he has been chairman of the "software chapter" of the RNRT funding programme of the french ministeries for research and telecommunications, for telecommunications (Reseau National de la Recherche en Telecommunications). Since 1997, he has been responsible for INRIA of the joint Alcatel-INRIA research programme and is now chief scientist of the joint Bell Labs-INRIA research lab. He is member of the scientific board of INRIA, in charge of embedded systems area. He has been member of the advisory board of T-Source, a venture capitalist specialist in seed capital for the telecommunications sector. He is a member of the scientific advisory boards of SAFRAN Group and France Telecom. Since June 2011, he is co-heading the Center of Excellence (Labex) CominLabs in the area of telecommunications and Information systems. He has been elected to the Académie des Technologies in december 2011.