A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

• Autorzy: Andreas Rauh , Michael Brill , Clemens Günther
• Języki publikacji: EN

Abstrakty

EN

The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.

Słowa kluczowe

EN

ordinary differential equations; differential-algebraic equations; VALENCIA-IVP; verified simulation; inverse control problems

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2009
• Tom: 19
• Numer: 3
• Strony: 381-397

Daty

wydano

2009

otrzymano

2008-09-22

poprawiono

2008-12-15

Twórcy

autor

Andreas Rauh

• Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany

autor

Michael Brill

• Institute of Measurement, Control, and Microtechnology, University of Ulm, D-89069 Ulm, Germany

autor

Clemens Günther

• Institute of Measurement, Control, and Microtechnology, University of Ulm, D-89069 Ulm, Germany

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Identyfikatory

DOI

10.2478/v10006-009-0032-4