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Parallel indirect solution of optimal control problems
Author(s) -
Fabien Brian C.
Publication year - 2013
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2064
Subject(s) - discretization , mathematics , residual , jacobian matrix and determinant , interior point method , factorization , algebraic equation , diagonal , speedup , optimal control , mathematical optimization , algorithm , computer science , parallel computing , mathematical analysis , physics , geometry , nonlinear system , quantum mechanics
SUMMARY This paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two‐point BVP with index‐1 differential‐algebraic equations (BVP‐DAEs). These BVP‐DAEs are solved using a multiple shooting method where the DAEs are approximated using a single‐step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior‐point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior‐point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel‐structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used. Copyright © 2013 John Wiley & Sons, Ltd.