Abstract
Coupling constraints and ordinary differential equations has numerous applications. This paper shows how to introduce constraints involving ordinary differential equations into the numerical constraint satisfaction problem framework in a natural and efficient way. Slightly adapted standard filtering algorithms proposed in the numerical constraint satisfaction problem framework are applied to these constraints leading to a branch and prune algorithm that handles ordinary differential equations based constraints. Preliminary experiments are presented.
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References
Raïssi, T., Ramdani, N., Candau, Y.: Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica 40(10), 1771–1777 (2004)
Granvilliers, L., Cruz, J., Barahona, P.: Parameter estimation using interval computations. SIAM J. Sci. Comput. 26(2), 591–612 (2005)
Kapela, T., Simó, C.: Computer assisted proofs for nonsymmetric planar choreographies and for stability of the eight. Nonlinearity 20(5), 1241 (2007)
Lin, Y., Stadtherr, M.A.: Guaranteed state and parameter estimation for nonlinear continuous-time systems with bounded-error measurements. Industrial & Engineering Chemistry Research 46(22), 7198–7207 (2007)
Johnson, T., Tucker, W.: Brief paper: Rigorous parameter reconstruction for differential equations with noisy data. Automatica 44(9), 2422–2426 (2008)
Lin, Y., Enszer, J.A., Stadtherr, M.A.: Enclosing all solutions of two-point boundary value problems for odes. Computers & Chemical Engineering 32(8), 1714–1725 (2008)
Cruz, J., Barahona, P.: Constraint Satisfaction Differential Problems. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 259–273. Springer, Heidelberg (2003)
Cruz, J., Barahona, P.: Constraint reasoning in deep biomedical models. Artificial Intelligence in Medicine 34(1), 77–88 (2005)
Moore, R.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge (1990)
Benhamou, F., Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. Journal of Logic Programming 32(1), 1–24 (1997)
Van Hentenryck, P., McAllester, D., Kapur, D.: Solving polynomial systems using a branch and prune approach. SIAM J. Numer. Anal. 34(2), 797–827 (1997)
Granvilliers, L.: A symbolic-numerical branch and prune algorithm for solving non-linear polynomial systems. Journal of Universal Computer Science 4(2), 125–146 (1998)
Goldsztejn, A., Goualard, F.: Box Consistency through Adaptive Shaving. In: Proc. of ACM SAC 2010, pp. 2049–2054 (2010)
Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I. Springer, Heidelberg (2000)
Nedialkov, N.S., Jackson, K.R., Corliss, G.F.: Validated Solutions of Initial Value Problems for Ordinary Differential Equations. Applied Mathematics and Computation 105(1), 21–68 (1999)
Janssen, M., Deville, Y., Hentenryck, P.V.: Multistep filtering operators for ordinary differential equations. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 246–260. Springer, Heidelberg (1999)
Zgliczynski, P.: C1-Lohner Algorithm. Foundations of Computational Mathematics 2(4), 429–465 (2002)
Goldsztejn, A., Hayes, W.: Reliable Inner Approximation of the Solution Set to Initial Value Problems with Uncertain Initial Value. In: Proceedings of SCAN 2006, p. 19. IEEE Press, Los Alamitos (2006)
Goldsztejn, A., Michel, C., Rueher, M.: Efficient Handling of Universally Quantified Inequalities. Constraints 14(1), 117–135 (2008)
Goldsztejn, A., Granvilliers, L.: A New Framework for Sharp and Efficient Resolution of NCSP with Manifolds of Solutionss. Constraints 15(2), 190–212 (2010)
Eveillard, D., Ropers, D., de Jong, H., Branlant, C., Bockmayr, A.: A multi-scale constraint programming model of alternative splicing regulation. Theor. Comput. Sci. 325(1), 3–24 (2004)
Carlson, B., Gupta, V.: Hybrid cc with interval constraints. In: HSCC 1998: Proceedings of the First International Workshop on Hybrid Systems, pp. 80–95 (1998)
Gupta, V., Jagadeesan, R., Saraswat, V.A.: Computing with continuous change. Sci. Comput. Program. 30(1-2), 3–49 (1998)
Kuzmic, P.: Program DYNAFIT for the Analysis of Enzyme Kinetic Data: Application to HIV Proteinase. Analytical Biochemistry 237(2), 260–273 (1996)
Mendes, P., Kell, D.: Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 14(10), 869–883 (1998)
Lin, Y., Stadtherr, M.A.: Validated solutions of initial value problems for parametric odes. Applied Numerical Mathematics 57(10), 1145–1162 (2007)
Hlavácek, V., Marek, M., Kubícek, M.: Modelling of chemical reactors – X multiple solutions of enthalpy and mass balances for a catalytic reaction within a porous catalyst particle. Chemical Engineering Science 23(9), 1083–1097 (1968)
Chen, Y.: Dynamic systems optimization. Ph. D. Thesis, University of California (2006)
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Goldsztejn, A., Mullier, O., Eveillard, D., Hosobe, H. (2010). Including Ordinary Differential Equations Based Constraints in the Standard CP Framework. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_20
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DOI: https://doi.org/10.1007/978-3-642-15396-9_20
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