From synchronous programs to symbolic representations of hybrid systems

Bauer, Kerstin; Schneider, Klaus

doi:10.1145/1755952.1755960

Cited by 9 publications

(6 citation statements)

References 37 publications

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“…In the present work, we adapted the simpler causality of Lustre and Lucid Synchrone based on a precedence relation in order to focus on the specific issues raised when mixing discrete and continuous-time signals. Schneider et al [26] have considered the causality problem for a hybrid extension of Quartz, a variant of Esterel with ODEs. But, they did not address issues arising from the interaction of discrete and continuous behaviors.…”

Section: Discussion and Related Workmentioning

confidence: 99%

A type-based analysis of causality loops in hybrid systems modelers

Benveniste

Bourke²,

Caillaud³

et al. 2017

Nonlinear Analysis: Hybrid Systems

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Explicit hybrid systems modelers like Simulink/Stateflow allow for programming both discrete-and continuous-time behaviors with complex interactions between them. An important step in their compilation is the static detection of algebraic or causality loops. Such loops can cause simulations to deadlock and prevent the generation of statically scheduled code. This paper addresses this issue for a hybrid modeling language that combines synchronous data-flow equations with Ordinary Differential Equations (ODEs). We introduce the operator last x for the left-limit of a signal x. The last x operator is used to break causality loops and permits a uniform treatment of discrete and continuous state variables. The semantics of the language relies on non-standard analysis, defining an execution as a sequence of infinitesimally small steps. A signal is deemed causally correct when it can be computed sequentially and only changes infinitesimally outside of announced discrete events like zero-crossings. The causality analysis takes the form of a type system that expresses dependencies between signals. In well-typed programs, signals are provably continuous during integration provided that imported external functions are also continuous, and sequential code can be generated. The effectiveness of the system is illustrated with several examples written in Zélus, a Lustre-like synchronous language extended with ODEs.

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Section: Discussion and Related Workmentioning

confidence: 99%

A type-based analysis of causality loops in hybrid systems modelers

Benveniste

Bourke²,

Caillaud³

et al. 2017

Nonlinear Analysis: Hybrid Systems

View full text Add to dashboard Cite

show abstract

“…In the present work, we adapted the simpler causality of Lustre and Lucid Synchrone based on a precedence relation in order to focus on specific issues raised when mixing discrete and continuous-time signals. Schneider et al [2] have considered the causality problem for a hybrid extension of Quartz, a variant of Esterel, with ODEs. But, they did not address issues due to the interaction of discrete and continuous behaviors.…”

Section: Discussion and Related Workmentioning

confidence: 99%

“…Tools for modeling hybrid systems [7] such as Modelica, 1 LabVIEW, 2 and Simulink/Stateflow, 3 are now rightly understood and studied as programming languages. Indeed, models are used not only for simulation, but also for test-case generation, formal verification and translation to embedded code.…”

Section: Causality and Schedulingmentioning

confidence: 99%

A type-based analysis of causality loops in hybrid systems modelers

Benveniste

Bourke

Caillaud

et al. 2014

Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control

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Explicit hybrid systems modelers like Simulink/Stateflow allow for programming both discrete-and continuous-time behaviors with complex interactions between them. A key issue in their compilation is the static detection of algebraic or causality loops. Such loops can cause simulations to deadlock and prevent the generation of statically scheduled code.This paper addresses this issue for a hybrid modeling language that combines synchronous data-flow equations with Ordinary Differential Equations (ODEs). We introduce the operator last(x) for the left-limit of a signal x. This operator is used to break causality loops and permits a uniform treatment of discrete and continuous state variables. The semantics relies on non-standard analysis, defining an execution as a sequence of infinitesimally small steps. A signal is deemed causally correct when it can be computed sequentially and only changes infinitesimally outside of announced discrete events like zero-crossings. The causality analysis takes the form of a type system that expresses dependences between signals. In well-typed programs, signals are provably continuous during integration provided that imported external functions are also continuous.The effectiveness of this system is illustrated with several examples written in Zélus, a Lustre-like synchronous language extended with hierarchical automata and ODEs.

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“…The idea is to design applications in discrete time and to show their correctness with respect to implementations modeled in continuous time. The semantics of Quartz programs have been defined using timed Kripke structures for the verification of timing properties [20] and more recently extended to treat hybrid systems [21]. Abstract interpretation techniques have been proposed to verify safety properties of synchronous models involving multiform timing characteristics linked by linear relations [22].…”

Section: Related Workmentioning

confidence: 99%

Symbolic Simulation of Dataflow Synchronous Programs with Timers

Baudart

Bourke²,

Pouzet³

2018

Lecture Notes in Electrical Engineering

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The synchronous language Lustre and its descendants have long been used to program and model discrete controllers. Recent work shows how to mix discrete and continuous elements in a Lustre-like language called Zélus. The resulting hybrid programs are deterministic and can be simulated with a numerical solver. In this article, we focus on a subset of hybrid programs where continuous behaviors are expressed using timers, nondeterministic guards, and invariants, as in Timed Safety Automata. We propose a source-to-source compilation pass to generate discrete code that, coupled with standard operations on Difference-Bound Matrices, produces symbolic traces that each represent a set of concrete traces.

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From synchronous programs to symbolic representations of hybrid systems

Cited by 9 publications

References 37 publications

A type-based analysis of causality loops in hybrid systems modelers

A type-based analysis of causality loops in hybrid systems modelers

A type-based analysis of causality loops in hybrid systems modelers

Symbolic Simulation of Dataflow Synchronous Programs with Timers

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