TY - JOUR

T1 - On the solution of differential-algebraic equations through gradient flow embedding

AU - del Rio-Chanona, Ehecatl Antonio

AU - Bakker, Craig

AU - Fiorelli, Fabio

AU - Paraskevopoulos, Michail

AU - Scott, Felipe

AU - Conejeros, Raúl

AU - Vassiliadis, Vassilios S.

N1 - Publisher Copyright:
© 2017 Elsevier Ltd

PY - 2017

Y1 - 2017

N2 - In this paper Gradient Flow methods are used to solve systems of differential-algebraic equations via a novel reformulation strategy, focusing on the solution of index-1 differential-algebraic equation systems. A reformulation is first effected on semi-explicit index-1 differential-algebraic equation systems, which casts them as pure ordinary differential equation systems subject to an embedded pointwise least-squares problem. This is then formulated as a gradient flow optimization problem. Rigorous proofs for this novel scheme are provided for asymptotic and epsilon convergence. The computational results validate the predictions of the effectiveness of the proposed approach, with efficient and accurate solutions obtained for the case studies considered. Beyond the theoretical and practical value for the solution of DAE systems as pure ODE ones, the methodology is expected to have an impact in similar cases where an ODE system is subjected to algebraic constraints, such as the Hamiltonian necessary conditions of optimality in optimal control problems.

AB - In this paper Gradient Flow methods are used to solve systems of differential-algebraic equations via a novel reformulation strategy, focusing on the solution of index-1 differential-algebraic equation systems. A reformulation is first effected on semi-explicit index-1 differential-algebraic equation systems, which casts them as pure ordinary differential equation systems subject to an embedded pointwise least-squares problem. This is then formulated as a gradient flow optimization problem. Rigorous proofs for this novel scheme are provided for asymptotic and epsilon convergence. The computational results validate the predictions of the effectiveness of the proposed approach, with efficient and accurate solutions obtained for the case studies considered. Beyond the theoretical and practical value for the solution of DAE systems as pure ODE ones, the methodology is expected to have an impact in similar cases where an ODE system is subjected to algebraic constraints, such as the Hamiltonian necessary conditions of optimality in optimal control problems.

KW - DAE

KW - Differential-algebraic equations

KW - Gradient flow

KW - Ordinary differential equations

KW - Semi-explicit index-1

UR - http://www.scopus.com/inward/record.url?scp=85017173115&partnerID=8YFLogxK

U2 - 10.1016/j.compchemeng.2017.03.020

DO - 10.1016/j.compchemeng.2017.03.020

M3 - Article

AN - SCOPUS:85017173115

VL - 103

SP - 165

EP - 175

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

ER -