{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,28]],"date-time":"2024-07-28T04:35:52Z","timestamp":1722141352603},"reference-count":19,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,9,1]]},"abstract":"Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems<\/jats:title>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.<\/jats:p>","DOI":"10.2478\/v10006-009-0039-x","type":"journal-article","created":{"date-parts":[[2009,9,29]],"date-time":"2009-09-29T10:04:23Z","timestamp":1254218663000},"page":"485-499","source":"Crossref","is-referenced-by-count":6,"title":["Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems"],"prefix":"10.61822","volume":"19","author":[{"given":"Mareile","family":"Freihold","sequence":"first","affiliation":[]},{"given":"Eberhard","family":"Hofer","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"key":"1","unstructured":"Bendsten, C. and Staunting, O. (2007). FADBAD++, Version 2.1, Available at: http:\/\/www.fadbad.com\/fadbad.html<\/a>"},{"key":"2","unstructured":"Boyd, S., Gosh, A. and Magnani, A. (2003). Branch and bound methods, Available at: http:\/\/www.stanford.edu\/class\/ee3920\/bb.pdf<\/a>"},{"key":"3","unstructured":"Clausen, J. (1999). Branch and bound algorithms: Principles and examples, Available at: citeseer.ist.psu.edu\/683497.html<\/a>"},{"key":"4","unstructured":"de Figueiredo, L. H., van Iwaarden, R. and Stolfi, J. (1997). Fast interval branch-and-bound methods for unconstrained global optimization with affine arithmetic, Technical Report IC-97-08<\/i>, Institute of Computing, University of Campinas, Campinas, Brazil."},{"key":"5","first-page":"58","article-title":"Extraction of rules for model based estimation of granulocytopoiesis","author":"E. Hofer","year":"1991a"},{"key":"6","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/978-3-642-77020-3_4","volume":"275","author":"E. 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(2008). Theorie und Anwendung von Intervall-methoden f\u00fcr Analyse und Entwurf robuster und optimaler Regelungen dynamischer Systeme<\/i>, Fortschritt-Berichte VDI, Reihe 8, Nr. 1148, PhD thesis, University of Ulm, Ulm, (in German)."},{"key":"14","article-title":"ValEncIA-IVP: A comparison with other initial value problem solvers","author":"A. Rauh","year":"2007"},{"key":"15","doi-asserted-by":"crossref","first-page":"381","DOI":"10.2478\/v10006-009-0032-4","article-title":"A novel interval arithmetic approach for solving differential-algebraic equations with ValEncIA-IVP","volume":"3","author":"A. Rauh","year":"2009","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"16","doi-asserted-by":"crossref","first-page":"2167","DOI":"10.1137\/040604388","article-title":"Bounding the solutions of parameter dependent nonlinear ordinary differential equations","volume":"6","author":"A. Singer","year":"2006","journal-title":"SIAM Journal on Scientific Computing"},{"key":"17","unstructured":"The American Heritage Medical Dictionary<\/i> (2007). Houghton Mifflin Company, Boston, MA."},{"key":"18","unstructured":"van der Schaft, A. J. (2005). Network modeling and control of physical systems, DISC theory of port-Hamiltonian systems, Available at: http:\/\/www.vf.utwente.nl\/~schaftaj\/downloads-diversen\/DISCportbased1.pdf<\/a>"},{"key":"19","unstructured":"van der Schaft, A. J. and Maschke, B. M. J. (2003). Port-Hamiltonian systems: A theory for modeling, simulation and control of complex physical systems, Available at: http:\/\/www-lar.deis.unibo.it\/eurongeoplex-sumsch\/files\/lectures_1\/VanDerSchaft\/VDSchaft_01_PCHS.pdf<\/a>"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/19\/3\/article-p485.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2009.19.issue-3\/v10006-009-0039-x\/v10006-009-0039-x.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:27:44Z","timestamp":1709202464000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-009-0039-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,1]]},"references-count":19,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/v10006-009-0039-x","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2009,9,1]]}}}