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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