time_optimal_rocket.cpp

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/*
 *    This file is part of ACADO Toolkit.
 *
 *    ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
 *    Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau,
 *    Milan Vukov, Rien Quirynen, KU Leuven.
 *    Developed within the Optimization in Engineering Center (OPTEC)
 *    under supervision of Moritz Diehl. All rights reserved.
 *
 *    ACADO Toolkit is free software; you can redistribute it and/or
 *    modify it under the terms of the GNU Lesser General Public
 *    License as published by the Free Software Foundation; either
 *    version 3 of the License, or (at your option) any later version.
 *
 *    ACADO Toolkit is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *    Lesser General Public License for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with ACADO Toolkit; if not, write to the Free Software
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */



#include <acado_optimal_control.hpp>
#include <acado_gnuplot.hpp>


int main( ){

    USING_NAMESPACE_ACADO


    // INTRODUCE THE VARIABLES:
    // -------------------------

    DifferentialState     s,v,m;
    Control               u    ;
    Parameter             T    ;

    DifferentialEquation  f( 0.0, T );


    // DEFINE A DIFFERENTIAL EQUATION:
    // -------------------------------

    f << dot(s) == v;
    f << dot(v) == (u-0.2*v*v)/m;
    f << dot(m) == -0.01*u*u;


    // DEFINE AN OPTIMAL CONTROL PROBLEM:
    // ----------------------------------
    OCP ocp( 0, T, 20 );

    ocp.minimizeMayerTerm( T );
    ocp.subjectTo( f );

    ocp.subjectTo( AT_START, s ==  0.0 );
    ocp.subjectTo( AT_START, v ==  0.0 );
    ocp.subjectTo( AT_START, m ==  1.0 );

    ocp.subjectTo( AT_END  , s == 10.0 );
    ocp.subjectTo( AT_END  , v ==  0.0 );

    ocp.subjectTo( -0.1 <= v <=  1.7  );
    ocp.subjectTo( -1.1 <= u <=  1.1  );
    ocp.subjectTo(  5.0 <= T <= 15.0  );


    // VISUALIZE THE RESULTS IN A GNUPLOT WINDOW:
    // ------------------------------------------
    GnuplotWindow window;
        window.addSubplot( s, "THE DISTANCE s"      );
        window.addSubplot( v, "THE VELOCITY v"      );
        window.addSubplot( m, "THE MASS m"          );
        window.addSubplot( u, "THE CONTROL INPUT u" );


    // DEFINE AN OPTIMIZATION ALGORITHM AND SOLVE THE OCP:
    // ---------------------------------------------------
    OptimizationAlgorithm algorithm(ocp);

    algorithm.set( MAX_NUM_ITERATIONS, 20 );
//      algorithm.set( HESSIAN_APPROXIMATION, EXACT_HESSIAN );
//      algorithm.set( HESSIAN_PROJECTION_FACTOR, 1.0 );
        
    algorithm << window;


//     algorithm.initializeDifferentialStates("tor_states.txt");
//     algorithm.initializeParameters("tor_pars.txt");
//     algorithm.initializeControls("tor_controls.txt");

    algorithm.solve();

//     algorithm.getDifferentialStates("tor_states.txt");
//     algorithm.getParameters("tor_pars.txt");
//     algorithm.getControls("tor_controls.txt");

    return 0;
}