Parallel Solution of Optimal-Control Problems by
Time-Domain Decomposition
Martin Berggren
FFA, the Aeronautical Research Institute of Sweden
Computational Aerodynamics Branch
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
M-O. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Periaux, and M. F.
Wheeler (eds.). Computational Science for the 21st Century. J. Wiley,
Chichester, 1997, pp. 102-112.
Abstract
A parallel method for optimal control problems governed
by time-dependent partial differential equations (PDEs)
is presented. The method is based on a decomposition
of the time-domain analogous to multiple shooting methods.
This results in a set of optimal control problems on
smaller time intervals that are coupled at the
time interval boundaries. This coupled system is
solved using a Gauss-Seidel method with a `red-black' ordering.
In each step this requires the parallel solution of smaller
optimal control problems which are of the same type as the
original one.
This approach requires no controllability assumptions
and is suited for optimal control problems governed by
time dependent PDEs.
Keywords
Time dependent optimal control problems,
time-domain decomposition, parallel solution.
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