Title: A continuation method for minimum time problems
Authors: Harri Ehtamo
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND
harri.ehtamo@hut.fi
www.sal.hut.fi/Personnel/Homepages/HarriE.html

Tuomas Raivio
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND
tuomas.raivio@hut.fi
www.sal.hut.fi/Personnel/Homepages/TuomasR.html

Raimo P. Hämäläinen
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND
raimo@hut.fi
www.sal.hut.fi/Personnel/Homepages/RaimoH.html

Date: March 2000
Status: Systems Analysis Laboratory Research Report E3 March 2000
Abstract: We present a continuation method for minimum time optimal control problems. The problem is turned into a sequence of terminal cost minimization problems with fixed final time that is used as the continuation parameter. The final time is corrected by a one-dimensional search procedure until the terminal condition becomes satisfied. The method is illustrated by two minimum time aircraft trajectory optimization problems.
Keywords: optimal control, multipoint boundary value problem, homotopy, minimum time control, aerospace applications.