%   
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; clc; clear; 

% set the constants of this problem: 
t_0     = 0.; 
t_f     = 10.; 
v_0     = 100.; % the initial conditions
gamma_0 = pi/2.; 
h_0     = 0;

v_d     = 5000; % the target goals
gamma_d = pi/3.;
h_d     = 20000;

q_v = 0.1; 
q_gamma = 10; % the error weighting factor for gamma(t_f) missing gamma_d 
q_h = 0.01;
r_1 = 1; % the error coefficient for the integral of alpha(t)
r_2 = 1;

% find the optimal value for [alpha,T]: 
%  
alphas = fminsearch( @(x) sect_3_prob_4_J_min_fn(x(1), x(2), t_0, t_f, v_0, gamma_0, h_0, v_d, gamma_d, h_d, q_v, q_gamma, q_h, r_1, r_2), [ 0., 0. ] );
alphas

% evaluate J at this value of alpha
sect_3_prob_4_J_min_fn(alphas(1), alphas(2), t_0, t_f, v_0, gamma_0, h_0, v_d, gamma_d, h_d, q_v, q_gamma, q_h, r_1, r_2)