Brachistochrone Optimal Control Problem
The brachistochrone optimal control problem is stated as follows. Minimize the cost functional
subject to the dynamic constraints
and the boundary conditions
The solution to the brachistochrone optimal control problem using GPOPS-II is shown in the figures below.
Image “Curve of the Red and White Roller Coaster Rail” Courtesy of FreeDigitalPhotos.net. Photo by Keerati. Used with Permission.
GPOPS-II: Next-Generation Optimal Control Software