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Date & Time:
Tuesday, April 5, 2022; 11:00 AM EDT
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Abstract:
Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In our introduction, will briefly explain why and when the approximate structural analysis implemented in current Modelica tools leads to such errors. Then we will present our multimode Pryce Sigma-method for index reduction, in which the mode-dependent Sigma-matrix is represented in a dual form, by attaching, to every valuation of the sigma_ij entry of the Sigma matrix, the predicate characterizing the set of modes in which sigma_ij takes this value. We will illustrate this multimode analysis on example, by using our IsamDAE tool. In a second part, we will complement this multimode DAE structural analysis by a new structural analysis of mode changes (and, more generally, transient modes holding for zero time). Also, mode changes often give raise to impulsive behaviors: we will present a compile-time analysis identifying such behaviors. Our structural analysis of mode changes deeply relies on nonstandard analysis, which is a mathematical framework in which infinitesimals and infinities are first class citizens.
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Speaker:
Albert Benveniste, Benoît Caillaud, and Mathias Malandain
Inria
Albert Benveniste performed his Thèse d'État in Mathematics, probability theory, in 1975. From 1979 to 2014 he has been Directeur de Recherche at INRIA, and he is Inria emeritus since then. In 1990 he received the CNRS silver medal and he has been elected IEEE fellow in 1991 and IFAC fellow in 2013. Since 2011, he is a member of the scientific advisory board of SAFRAN Group. From 2011 to 2020, he was member of the scientific advisory board of Orange, and president of the scientific council of Orange for 2018-2020. He has been elected to the Académie des Technologies (French National Academy of Engineering) in December 2011. His competences include topics in: signal processing and control; vibration mechanics; reactive, real-time, and embedded systems design in computer science (until 2010). His current interests are the design of hybrid systems modelers and particularly Modelica, based on non-standard analysis semantics.
Benoît Caillaud graduated from École Normale Supérieure (Paris, France) in 1990. He received a PhD in Computer Science from the University of Rennes 1 in 1994 and a Habilitation à Diriger les Recherches from the University of Rennes 1 in 2011. After a postdoc at the University of Edinburgh, he joined Inria in 1997 as a researcher. From 2002 until 2012 he has been in charge of the S4 team on Embedded Systems Design, at Inria. He is now senior researcher at Inria, head of the Hycomes team on Hybrid Systems Modeling and Verification. From 2015 until 2021, he has been head of the Language & Software Engineering department of IRISA. His main research interests are hybrid systems modeling and contract-based reasoning for cyber-physical systems design. His current research focuses on the design of scalable structural analysis algorithm for the compilation and simulation of large multimode Modelica models.
Mathias Malandain is Expert Engineer (Mathematics & Software Engineering) at Inria since 2018. He received a PhD in Numerical Analysis (2013, INSA Rouen, France, with applications to the simulation of incompressible fluid flows). Until 2018, he has been teaching mathematics in French public middle-/high-schools. His current scientific focus is on the compile-time analysis of large-scale multimode Modelica models and include the design and implementation of novel algorithms for the structural analysis of the underlying mathematical systems.
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MERL Host:
Scott A. Bortoff
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Research Areas:
Dynamical Systems, Multi-Physical Modeling