Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems
Interval arithmetic techniques such as ValEncIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algori...
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| Vydané v: | International Journal of Applied Mathematics and Computer Science Ročník 19; číslo 3; s. 485 - 499 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Zielona Góra
Versita
01.09.2009
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services |
| Predmet: | |
| ISSN: | 1641-876X, 2083-8492 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Interval arithmetic techniques such as ValEncIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically meaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics. |
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| Bibliografia: | v10006-009-0039-x.pdf istex:6E5BF9AEFCA5CEFDB6D6EDE3EE705E99A63D8943 ArticleID:v10006-009-0039-x ark:/67375/QT4-X3DZZLTJ-F ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1641-876X 2083-8492 |
| DOI: | 10.2478/v10006-009-0039-x |