Cyber-Physical Systems modeling languages

We address the design of hybrid system modeling languages, supporting the rigorous design of Cyber-Physical Systems. The team investigates the following two directions:

• The compilation of acausal modeling languages, such as Modelica (Simscape and Amesim being other industrially used instances). These languages rely on Differential Algebraic Equations (DAE), not ODE. DAE-based languages have better support for physical modeling from the first principles of physics, and allow for seamless reuse of models from libraries. Such languages support the specification of different modes with different DAE dynamics, together with mode changes conditions.
• The study of non-smooth systems models and compilation of related languages, which are hybrid system modeling techniques allowing for multimode dynamics without the need for explicitly specifying the different modes. Instead, hybrid behaviors are specified using non-smooth operators such as complementarity conditions or Filippov dynamics.

Compilation of DAE-based modeling languages

DAE-based modeling languages such as Modelica offer multimode modeling, in which different modes are specified with different DAE dynamics, and time- and/or state-triggered mode switching. Simulating such models requires detecting mode changes, performing restarts, and approximating the due DAE dynamics in each mode. Code generation for DAE-based languages requires a difficult symbolic pre-processing called index reduction, which is performed via structural analysis.

Simulation and code generation of pure DAE models (having a single mode) is well understood. Multimode DAE models, however, are not well supported. Some physically meaningful models simulate correctly, some do not (models with mode-dependent structure or index are typically problematic). As a consequence, DAE-based modeling requires dedicated expertise in model twisting to accommodate the above problems.

Two main root causes for such problems were identified:

1. the structural analysis performed by existing tools is not a multimode analysis per se;
2. the handling of mode changes can be incorrect.

Our team focuses on addressing these two issues, both regarding the fundamentals, and in developing effective algorithms, implemented or under development in the IsamDAE software. One important objective is to be able to identify, at compile time, if parts of a given model can be under- or over-specified.

Participants

Albert Benveniste, Benoît Caillaud, Khalil Ghorbal, Mathias Malandain (research engineer).

Major collaborations

On mathematics, including the structural analysis of DAE models, we are in close contact with John Pryce (University of Cardiff, UK). Regarding Modelica and its design, we cooperate with Hilding Elmqvist (formerly Dassault Systèmes Lund) and Martin Otter (DLR, München). A tight collaboration with Dassault Systèmes in Lund, where the commercial Modelica tool Dymola is developed, is at the core of the FUI Modeliscale project.

Contracts and funding

IPL Modeliscale

Information about the IPL (Inria Project Lab) Modeliscale can be found here.

FUI Modeliscale

The FUI (Fonds Unique Interministériel) Modeliscale is a collaborative R&D project funded by the French government. The main objective of this project is the development of new Modeling & Simulation (M&S) solutions for large-scale energy networks, which are typically multimode, reconfigurable and multiscale systems. This collaboration involves Dassault Systèmes, EDF, ENGIE, CEA/INES, DPS, Eurobios and Phimeca.
A presentation of the project (in French) can be found here.

Publications

The list of publications about this topic can be found here.

Software

The IsamDAE software is described here.

Complementarity conditions and nonsmooth DAE systems

Complementarity Conditions (CC) are the core of models for ideal diodes in electric circuits, ideal contact in mechanics, and more physical phenomena. They have the generic form: both the flow and effort are non-negative, and their product is always zero. The whole is seen as a single non-smooth equation, which can be combined with other CC and other equations including ODEs/DAEs. This defines a subclass of multimode systems with no need to explicitly specify the different modes. A large litterature exists, both for the non-smooth systems in the different physics, and for their numerical schemes.

Wellposedness conditions (ensuring existence and uniqueness of solution) for CC-based systems are known for Linear Complementarity Systems (LCS) but their effective checking is very costly. A rank type of conditions, called relative degree, exists for LCS; this is reminiscent of the notions of index and structural analysis for DAEs. Our objective is to identify corresponding notions, for CC-based systems. This will pave the way toward including CCs as a primitive of DAE-based modeling languages.

Participants

Khalil Ghorbal, Christelle Kozaily (PhD).

Major collaborations

In the context of the IPL ModeliScale, this topic is addressed in cooperation with Vincent Acary, Bernard Brogliato and Alexandre Rocca (post-doc) from the Tripop team, Inria Grenoble.

Contracts and funding

IPL Modeliscale

Information about the IPL (Inria Project Lab) Modeliscale can be found here.

Publications

The list of publications about this topic can be found here.