Apps

Rocket Launch: Classic Optimal Control

Apps.RocketLaunch History

Show minor edits - Show changes to markup

August 26, 2016, at 05:14 PM by 10.5.113.104 -
August 26, 2016, at 05:13 PM by 10.5.113.104 -
Added lines 6-29:

Problem Statement

 minimize tf

 subject to
   ds/dt = v
   dv/dt = (u-0.2*v^2)/m
   dm/dt = -0.01 * u^2

 path constraints
   0.0 <= v(t) <= 1.7
   -1.1 <= u(t) <= 1.1

 initial boundary conditions
   s(0) = 0
   v(0) = 0
   m(0) = 1

 final boundary conditions
   s(tf) = 10.0
   v(tf) = 0.0

Solution

August 26, 2016, at 04:51 PM by 10.5.113.104 -
Changed lines 13-30 from:
to:

(:html:)

 <div id="disqus_thread"></div>
    <script type="text/javascript">
        /* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
        var disqus_shortname = 'apmonitor'; // required: replace example with your forum shortname

        /* * * DON'T EDIT BELOW THIS LINE * * */
        (function() {
            var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
            dsq.src = 'http://' + disqus_shortname + '.disqus.com/embed.js';
            (document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
        })();
    </script>
    <noscript>Please enable JavaScript to view the <a href="http://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>
    <a href="http://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>

(:htmlend:)

August 26, 2016, at 04:49 PM by 10.5.113.104 -
Added lines 1-13:

(:title Rocket Launch: Classic Optimal Control:) (:keywords Python, MATLAB, nonlinear control, Rocket, Goddard, model predictive control, dynamic programming:) (:description Minimize final time for rocket launch by manipulating the force exerted by the thruster. This is a classic dynamic optimization problem benchmark used in many research papers to test the application of new algorithms.:)

A rocket burn trajectory is desired to minimize a travel time between a starting point and a final point, 10 units of distance away. The thrust can be between an upper limit of 1.1 and a lower limit of -1.1. The initial and final velocity must be zero and the maximum velocity can never exceed 1.7. It is also desirable to minimize the use of fuel to perform the maneuver. There is a drag resistance the is proportional to the square of the velocity and mass is lost as the fuel is burned during thrust operations.

(:html:) <iframe width="560" height="315" src="https://www.youtube.com/embed/9qsiCGpvwKA" frameborder="0" allowfullscreen></iframe> (:htmlend:)