Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

Freihold, Mareile; Hofer, Eberhard P.

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

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Title: Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

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AMCS, volume 19 (2009)

Abstract:

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.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Resource Identifier:

oai:zbc.uz.zgora.pl:78784

DOI:

10.2478/v10006-009-0039-x

Pages:

485-499

Source:

AMCS, volume 19, number 3 (2009) ; click here to follow the link

Language:

eng

Rights:

Biblioteka Uniwersytetu Zielonogórskiego

Subject and keywords:

VALENCIA-IVP consistency tests for the reduction of overestimation identification of dynamical constraints Hamiltonian systems branch and prune algorithms

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Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering

Digital Library of Zielona Góra > Repository > Types of work > Articles

Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2009)

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Apr 9, 2024

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Apr 9, 2024

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https://zbc.uz.zgora.pl/publication/88560

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International Journal of Applied Mathematics and Computer Science (AMCS)

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