Towards a universal formalism for modeling & simulation
Article No.: 52, Pages 1 - 12
Abstract
The representation of hybrid systems has shown to be one of the greatest challenges in Modeling & simulation. While discrete event systems can be represented without error, continuous models rely on approximations based in numerical methods. Given the large variety of numerical integrators a unified representation has been elusive due the lack of an universal formalism that can describe all numerical methods and to provide their seamless integration. In this paper, we propose the Hybrid Flow System Specification (HyFlow) as a unifying representation for different families of numerical integrators for solving ordinary differential equations (ODEs). HyFlow combines the conventional discrete event approach with a novel representation based on sampling and the support for dense outputs to describe modular and hierarchical hybrid systems. We demonstrate that HyFlow can describe 1st-order, geometric (2nd-order), and exponential integrators. Additionally, since these integrators share the same underlaying HyFlow representation they can be seamlessly combined.
References
[1]
Abelman, S., and K. Patidar. 2008. "Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations". Computers and Mathematics with Applications 55:733--744.
[2]
Ascher, U., and L. Petzold. 1988. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM.
[3]
Barros, F. 2003. "Dynamic Structure Multiparadigm Modeling and Simulation". ACM Transactions on Modeling and Computer Simulation 13 (3): 259--275.
[4]
Barros, F. 2005a. "Simulating the Data Generated by a Network of Track-While-Scan Radars". In 12th Annual IEEE International Conference on Engineering Computer- Based Systems, 373--377.
[5]
Barros, F. 2005b. "A System Theory Approach to the Representation of Mobile Digital Controllers Agents". In International Workshop on Radical Agent Concepts.
[6]
Barros, F. 2008. "Semantics of Discrete Event Systems". In Distributed Event-Based Systems, 252--258.
[7]
Barros, F. 2015a. "Asynchronous, Polynomial ODE Solvers based on Error Estimation". In Symposium on Theory of Modeling and Simulation.
[8]
Barros, F. 2015b. "A modular representation of Fluid Stochastic Petri Nets". In Symposium on Theory of Modeling and Simulation, 122--128.
[9]
Benveniste, A., and G. Berry. 1991. "The Synchronous Approach to Reactive and Real-Time Systems". Proceedings of the IEEE 79 (9): 1270--1282.
[10]
Brock, P., and F. Murray. 1952. "The use of Exponential Sums in Step by Step Integration". Mathematics of Computation:63--78.
[11]
Certaine, J. 1959. Mathematical Methods for Digital Computers, Volume 1, Chapter The Solution of Ordinary Differential Equations with Large Time Constants, 128--132. John Wiley.
[12]
Fritzson, P. 2003. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley.
[13]
Hairer, E. 1997. "Variable time step integration with Symplectic methods". SIAM Journal of Scientific Computation 26 (6): 1838--1851.
[14]
Hairer, E., C. Lubich, and G. Wanner. 2005. Geometrical Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer.
[15]
Hairer, E., S. Nörsett, and G. Wanner. 2000. Solving Ordinary Differential Equations II: Stiff Problems. Springer.
[16]
Henzinger, T. 1996. "The Theory of Hybrid Automata". In 11th Annual IEEE Symposium on Logic in Computer Science, 278--292.
[17]
Hochbruck, M. 2010. "Exponential Integrators". Acta Numerica:209--286.
[18]
König, D., P. King, G. Laforge, H. D'Arcy, C. Champeau, E. Pragt, and J. Skeet. 2015. Groovy in Action. Manning.
[19]
Lynch, N., R. Segala, and F. Vaandrager. 2003. "Hybrid I/O Automata". Information and Computation 185:105--157.
[20]
Manna, Z., and A. Pnueli. 1993. "Verifying Hybrid Systems". In Formal Techniques in Real-Time and Fault-Tolerant Systems, 4--35.
[21]
Migoni, G., M. Bortolotto, E. Kofman, and F. Cellier. 2013. "Linearly implicit quantization-based integration methods for stiff ordinary differential equations". Simulation Modelling Practice and Theory 35:118--136.
[22]
Neta, B., and C. Ford. 1984. "Families of Methods for Ordinary Differential Equations based on Trigonometric Polynomials". Journal of Computational and Applied Mathematics 22:33--38.
[23]
Pope, D. A. 1963. "An Exponential Method of Numerical Integration of Ordinary Differential Equations". Communications of the ACM 6 (8): 491--493.
[24]
Praehofer, H. 1991. System Theoretic Foundations for Combined Discrete-Continuous System Simulation. Ph.d. diss., University of Linz, Austria.
[25]
Schierz, T., M. Arnold, and C. Clauss. 2006. "Co-simulation with communication step size control in an FMI compatible master algorithm". In Proceedings of the 9th International Modelica Conference, 205--214.
[26]
Skelboe, S. 2006. "Adaptive Partitioning Techniques for Ordinary Differential Equations". BIT Numerical Mathematics 46:617--629.
[27]
Stoffer, D. 1995. "Variable Steps for Reversible Integration Methods". Computing 55:1--22.
[28]
Swope, W. C., H. C. Andersen, P. H. Berens, and K. R. Wilson. 1982. "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters". Journal of Chemical Physics 76 (1): 637--649.
[29]
Zeigler, B. 1976. Theory of Modelling and Simulation. Wiley.
[30]
Zeigler, B., and J. Lee. 1998. "Theory of Quantized Systems: Formal Basis for DEVS/HLA Distributed Simulation Environment". In Proceedings of the SPIE: Enabling Technology for Simulation Science II, Volume 3369, 49--58.
- Towards a universal formalism for modeling & simulation
Recommendations
Integrated hybrid systems modeling and simulation methodology based on HDEVS formalism
SCSC '13: Proceedings of the 2013 Summer Computer Simulation ConferenceA hybrid system is a combination of subsystems that have different types of state and time: A typical example is a combination of discrete event and continuous system. A Hybrid Discrete EVent Systems specification (HDEVS) formalism approach was proposed ...
Equation-based modelling and simulation of hybrid systems
EOOLT '17: Proceedings of the 8th International Workshop on Equation-Based Object-Oriented Modeling Languages and ToolsEquation-based 1 modelling of hybrid systems has to consider dynamical systems consisting of components with continuous and/or discrete behavior. The paper focuses on such systems under special consideration of systems with variable model structure. ...
Composition of numerical integrators in the HyFlow formalism
WSC '18: Proceedings of the 2018 Winter Simulation ConferenceThe representation of complex Cyber-Physical Systems usually requires the ability to combine models described in different modeling formalisms and involving several numerical methods. While ordinary differential equations (ODEs) are a common formalism ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
December 2017
4389 pages
ISBN:9781538634271
Sponsors
Publisher
IEEE Press
Publication History
Published: 03 December 2017
Check for updates
Qualifiers
- Research-article
Conference
WSC '17
Sponsor:
Acceptance Rates
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 20Total Downloads
- Downloads (Last 12 months)1
- Downloads (Last 6 weeks)0
Reflects downloads up to 21 Nov 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in