Section: New Results

Hybrid Synchronous Languages

Participants : Timothy Bourke, Jun Inoue, Antoine Madet, Marc Pouzet.

During year 2013, we mainly worked on three directions: (a) the treatment of DAEs; (b) the design and implementation of a causality analysis for hybrid systems modelers; (c) the study of numerical techniques for non-smooth dynamical systems.

DAEs

As part of our participation in the European project MODRIO and SYS2SOFT projects, we have been developing a prototype for simulating DAE (Differential-Algebraic Equations) systems. DAEs are the basis of the language Modelica and their interaction with discrete features — in particular the novel ones introduced in 2012, like hierarchical automata and clocks — raise difficult semantical and compilation issues. The goal is to precisely define the interaction between synchronous programming constructs and DAEs, in term of semantics and compilation. One strong difficulty at the moment is that existing techniques (index reduction, dymmy derivative) are not modular and force, either to (a) write an interpretor where index reduction is done dynamically every time a mode change occurs or (b) statically enumerate all the modes, performing index reduction for every of those. While the first technique is too slow in practice (and it is not used in the most advanced Modelica compiler), the second one may explode in practice (putting $n$ two-state automata in parallel lead to $2^n$ states to be enumerated). During year 2013, we have investigated a new approach for index reduction.

Work to-date has focused on implementing standard algorithms from the literature (notably Pantelides, Dummy Derivatives, Dynamic State Selection). Despite the importance of these algorithms to tools like Modelica, we found that important implementation details and “tricks” are not always well documented.

This work is developed hand-in-hand with the interface to the Sundials IDA solver.

Causality Analysis

We have designed a causality analysis for a language that mix stream equations, hierarchical automata and ODEs and implemented it in the Zélus compiler. Its purpose is to give a sufficient condition for a hybrid program can be turned into statically scheduled code. Moreover, the analysis ensures that absence of discontinuities outside of declared zero-crossing events. This result is novel and the proof deeply rely on the use of non standard analysis introduced in our previous works. This new result has been accepted for publication at HSCC 2014.

Non Smooth Dynamical Systems

In parallel, we collaborate with Bernard Brogliato and Vincent Acary (Inria team BIBOP, Grenoble) on non smooth dynamical systems. Beside general-purpose techniques for solving DAEs and implemented in Modelica compilers, there exist dedicated methods for systems with a lot of discontinuities and contacts (in mechanical system, electrical analogous circuits, etc.). They are far more efficient and numerically accurate than general-purpose techniques when the number of contact is important (e.g., transient in electrical circuits, a bag of marbles). They are based on a time stepping execution and do not have to stop at every zero-crossing event. The combination of those techniques with event detection ones (as used in the Simulink tool) is largely unknown. We are currently inverstigating the extension of our previous work to take Brogliato and Acary techniques into account. This is a novel but promising direction of research for the year to come.

In this research activity, we develop the new language Zélus used as a laboratory for experimenting novel programming constructs and compilation techniques. It serves to illustrate our research as Lucid Synchrone did in the past.

In collaboration with Benoit Caillaud and Albert Benveniste of the Inria HYCOMES team.