Modeling of dynamic systems
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Information and Computation
Introduction to Physical System Dynamics
Introduction to Physical System Dynamics
Constructive Semantics of Esterel: From Theory to Practice (Abstract)
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
Proceedings of the Real-Time: Theory in Practice, REX Workshop
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Languages and tools for hybrid systems design
Foundations and Trends in Electronic Design Automation
Leveraging synchronous language principles for heterogeneous modeling and design of embedded systems
EMSOFT '07 Proceedings of the 7th ACM & IEEE international conference on Embedded software
Actors without Directors: A Kahnian View of Heterogeneous Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Modelling of Complex Systems: Systems as Dataflow Machines
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Modeling time in hybrid systems: how fast is "instantaneous"?
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Divide and recycle: types and compilation for a hybrid synchronous language
Proceedings of the 2011 SIGPLAN/SIGBED conference on Languages, compilers and tools for embedded systems
Operational semantics of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A framework for comparing models of computation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Exercises in nonstandard static analysis of hybrid systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Hyperstream processing systems: nonstandard modeling of continuous-time signals
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Zélus: a synchronous language with ODEs
Proceedings of the 16th international conference on Hybrid systems: computation and control
Determinate composition of FMUs for co-simulation
Proceedings of the Eleventh ACM International Conference on Embedded Software
Automatica (Journal of IFAC)
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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 @e and @h in the celebrated generic sentence @?@e@?@h... 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).