Single shooting method example

An example of solving constrained optimization problem with single shooting method.

% This code demonstrates an example of solving constrained optimization problem
% with single shooting method.
% Constrained Optimization Problem:
% minimize L = 1/2 * integral_from_t0_to_T of (u.^2)
% Subject to: x_dot = (x2; u); with x = (x1, x2)
% initial value x(0) = (0; 1);
% final value x(T) = (0; -1);
% inequality constraint: x1 < 1/9;