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-// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
-/*
-
-    This is an example illustrating the use of the linear model predictive
-    control tool from the dlib C++ Library.  To explain what it does, suppose
-    you have some process you want to control and the process dynamics are
-    described by the linear equation:
-        x_{i+1} = A*x_i + B*u_i + C
-    That is, the next state the system goes into is a linear function of its
-    current state (x_i) and the current control (u_i) plus some constant bias or
-    disturbance.  
-                
-    A model predictive controller can find the control (u) you should apply to
-    drive the state (x) to some reference value, which is what we show in this
-    example.  In particular, we will simulate a simple vehicle moving around in
-    a planet's gravity.  We will use MPC to get the vehicle to fly to and then
-    hover at a certain point in the air.
-    
-*/
-
-
-#include <dlib/gui_widgets.h>
-#include <dlib/control.h>
-#include <dlib/image_transforms.h>
-
-
-using namespace std;
-using namespace dlib;
-
-//  ----------------------------------------------------------------------------
-
-int main()
-{
-    const int STATES = 4;
-    const int CONTROLS = 2;
-
-    // The first thing we do is setup our vehicle dynamics model (A*x + B*u + C).
-    // Our state space (the x) will have 4 dimensions, the 2D vehicle position
-    // and also the 2D velocity.  The control space (u) will be just 2 variables
-    // which encode the amount of force we apply to the vehicle along each axis.
-    // Therefore, the A matrix defines a simple constant velocity model.
-    matrix<double,STATES,STATES> A;
-    A = 1, 0, 1, 0,  // next_pos = pos + velocity
-        0, 1, 0, 1,  // next_pos = pos + velocity
-        0, 0, 1, 0,  // next_velocity = velocity
-        0, 0, 0, 1;  // next_velocity = velocity
-
-    // Here we say that the control variables effect only the velocity. That is,
-    // the control applies an acceleration to the vehicle.
-    matrix<double,STATES,CONTROLS> B;
-    B = 0, 0,
-        0, 0,
-        1, 0,
-        0, 1;
-
-    // Let's also say there is a small constant acceleration in one direction.
-    // This is the force of gravity in our model. 
-    matrix<double,STATES,1> C;
-    C = 0,
-        0,
-        0,
-        0.1;
-
-
-    const int HORIZON = 30;
-    // Now we need to setup some MPC specific parameters.  To understand them,
-    // let's first talk about how MPC works.  When the MPC tool finds the "best"
-    // control to apply it does it by simulating the process for HORIZON time
-    // steps and selecting the control that leads to the best performance over
-    // the next HORIZON steps.
-    //  
-    // To be precise, each time you ask it for a control, it solves the
-    // following quadratic program:
-    //   
-    //     min     sum_i trans(x_i-target_i)*Q*(x_i-target_i) + trans(u_i)*R*u_i 
-    //    x_i,u_i
-    //
-    //     such that: x_0     == current_state 
-    //                x_{i+1} == A*x_i + B*u_i + C
-    //                lower <= u_i <= upper
-    //                0 <= i < HORIZON
-    //
-    // and reports u_0 as the control you should take given that you are currently
-    // in current_state.  Q and R are user supplied matrices that define how we
-    // penalize variations away from the target state as well as how much we want
-    // to avoid generating large control signals.  We also allow you to specify
-    // upper and lower bound constraints on the controls.  The next few lines
-    // define these parameters for our simple example.
-
-    matrix<double,STATES,1> Q;
-    // Setup Q so that the MPC only cares about matching the target position and
-    // ignores the velocity.  
-    Q = 1, 1, 0, 0;
-
-    matrix<double,CONTROLS,1> R, lower, upper;
-    R = 1, 1;
-    lower = -0.5, -0.5;
-    upper =  0.5,  0.5;
-
-    // Finally, create the MPC controller.
-    mpc<STATES,CONTROLS,HORIZON> controller(A,B,C,Q,R,lower,upper);
-
-
-    // Let's tell the controller to send our vehicle to a random location.  It
-    // will try to find the controls that makes the vehicle just hover at this
-    // target position.
-    dlib::rand rnd;
-    matrix<double,STATES,1> target;
-    target = rnd.get_random_double()*400,rnd.get_random_double()*400,0,0;
-    controller.set_target(target);
-
-
-    // Now let's start simulating our vehicle.  Our vehicle moves around inside
-    // a 400x400 unit sized world.
-    matrix<rgb_pixel> world(400,400);
-    image_window win;
-    matrix<double,STATES,1> current_state;
-    // And we start it at the center of the world with zero velocity.
-    current_state = 200,200,0,0;
-
-    int iter = 0;
-    while(!win.is_closed())
-    {
-        // Find the best control action given our current state.
-        matrix<double,CONTROLS,1> action = controller(current_state);
-        cout << "best control: " << trans(action);
-
-        // Now draw our vehicle on the world.  We will draw the vehicle as a
-        // black circle and its target position as a green circle.  
-        assign_all_pixels(world, rgb_pixel(255,255,255));
-        const dpoint pos = point(current_state(0),current_state(1));
-        const dpoint goal = point(target(0),target(1));
-        draw_solid_circle(world, goal, 9, rgb_pixel(100,255,100));
-        draw_solid_circle(world, pos, 7, 0);
-        // We will also draw the control as a line showing which direction the
-        // vehicle's thruster is firing.
-        draw_line(world, pos, pos-50*action, rgb_pixel(255,0,0));
-        win.set_image(world);
-
-        // Take a step in the simulation
-        current_state = A*current_state + B*action + C;
-        dlib::sleep(100);
-
-        // Every 100 iterations change the target to some other random location. 
-        ++iter;
-        if (iter > 100)
-        {
-            iter = 0;
-            target = rnd.get_random_double()*400,rnd.get_random_double()*400,0,0;
-            controller.set_target(target);
-        }
-    }
-}
-
-//  ----------------------------------------------------------------------------
-