The Method of Orienting Curves and its Applications

Hoang Xuan Phu

Institute of Mathematics
Vietnamese Academy of Science and Technology
18 Hoang Quoc Viet Road, Hanoi, Vietnam

hxphu@math.ac.vn
http://hpsc.iwr.uni-heidelberg.de/hxphu/


Abstract:
The method of orienting curves, which was developed for solving
optimal control problems with state constraints, is presented
together with some applications, such as 
 - a Steiner's problem of finding an inpolgon with minimal circumference, 
 - a Zermelo's navigation problem, 
 - optimal control of a hydroelectric power plant,
 - an inventory problem, 
 - time-optimal control of manipulator along a prescribed trajectory,
 - finding the convex envelope of finite planar points.