Optimal Control Using Control Vector Parameterization

An example of using control vector parameterization to solve an optimal control problem

Description

File to run: mainproc.m

Control vector parameterization, also known as direct sequential method,
is one of the direct optimization methods for solving optimal control problems. The basic idea of direct optimization methods is to discretize the control problem, and then apply nonlinear programming (NLP) techniques to the resulting finite-dimensional optimization problem.

The problem is that you wish to steer from point $A=(0,0)$ at time $t = 0$ to close to point $B=(4,4)$ at time T. The motion takes place in the $x_1, x_2$ plane. Your control variables are thrust $u$ and angle of thrust $\theta$. The angle $\theta$ is measured from the $x_1$ axis. To make life interesting there is large mass at (3,0) that exerts a force proportional to the inverse of the square of the distance you are from the mass. (See published code for details)

* The problem is from a Optimal Control course (by Dr. Stephen Campbell) at NCSU.

• Required Products: Optimization Toolbox; MATLAB
• MATLAB release: MATLAB 7.12 (R2011a)
• Other requirements: Need Global Optimization Toolbox to run main_multistart.m