On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis

Justyna Zander; Pieter J. Mosterman; Gregoire Hamon; Ben Denckla

doi:10.3182/20110828-6-it-1002.02485

On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis

Abstract

Hybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches are employed to derive behaviors that approximate the analytic solution. An important part of this is the approximation of differential equation behavior by numerical integration. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially when repeated over iterations. This work formally defines the computational semantics of a solver in a denotational sense so as to analyze discrete- and continuous-time behavior of time-based block diagram models. A stream-based approach is used to analyze the numerical integration implemented by the solver. The resulting solver applies the principle of nonmonotonic time, which means that every new evaluation of values is computed in a temporally nonmonotonic manner. This allows for shifting the evaluation points backward and forward in time. A partially ordered structure is recovered based on the concept of stratification. Solver dynamics are thus made explicit and can be studied in concert with behavior of discontinuous models parts

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Authors (4)

Justyna Zander dr inż.
Pieter J. Mosterman
- MathWorks MathWorks
Gregoire Hamon
- MathWorks MathWorks
Ben Denckla
- Denckla Denckla

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Category:: Conference activity
Type:: publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
Title of issue:: Proceedings of the 18th IFAC World Congress, 2011 strony 9419 - 9424
Language:: English
Publication year:: 2011
Bibliographic description:: Zander J., Mosterman P., Hamon G., Denckla B.: On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis// Proceedings of the 18th IFAC World Congress, 2011/ Milano: , 2011, s.9419-9424
DOI:: Digital Object Identifier (open in new tab) 10.3182/20110828-6-it-1002.02485
Verified by:: Gdańsk University of Technology