00001 /* 00002 * This file is part of ACADO Toolkit. 00003 * 00004 * ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization. 00005 * Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau, 00006 * Milan Vukov, Rien Quirynen, KU Leuven. 00007 * Developed within the Optimization in Engineering Center (OPTEC) 00008 * under supervision of Moritz Diehl. All rights reserved. 00009 * 00010 * ACADO Toolkit is free software; you can redistribute it and/or 00011 * modify it under the terms of the GNU Lesser General Public 00012 * License as published by the Free Software Foundation; either 00013 * version 3 of the License, or (at your option) any later version. 00014 * 00015 * ACADO Toolkit is distributed in the hope that it will be useful, 00016 * but WITHOUT ANY WARRANTY; without even the implied warranty of 00017 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00018 * Lesser General Public License for more details. 00019 * 00020 * You should have received a copy of the GNU Lesser General Public 00021 * License along with ACADO Toolkit; if not, write to the Free Software 00022 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 00023 * 00024 */ 00025 00026 00033 #include <acado_optimal_control.hpp> 00034 #include <acado_gnuplot.hpp> 00035 00036 00037 /* >>> start tutorial code >>> */ 00038 int main( ){ 00039 00040 USING_NAMESPACE_ACADO 00041 00042 // INTRODUCE THE VARIABLES: 00043 // ------------------------- 00044 DifferentialState v,s,m; 00045 Control u ; 00046 DifferentialEquation f ; 00047 00048 const double t_start = 0.0; 00049 const double t_end = 10.0; 00050 00051 // DEFINE A DIFFERENTIAL EQUATION: 00052 // ------------------------------- 00053 00054 f << dot(s) == v; 00055 f << dot(v) == (u-0.02*v*v)/m; 00056 f << dot(m) == -0.01*u*u; 00057 00058 00059 // DEFINE AN OPTIMAL CONTROL PROBLEM: 00060 // ---------------------------------- 00061 OCP ocp( t_start, t_end, 20 ); 00062 ocp.minimizeLagrangeTerm( u*u ); 00063 ocp.subjectTo( f ); 00064 00065 ocp.subjectTo( AT_START, s == 0.0 ); 00066 ocp.subjectTo( AT_START, v == 0.0 ); 00067 ocp.subjectTo( AT_START, m == 1.0 ); 00068 ocp.subjectTo( AT_END , s == 10.0 ); 00069 ocp.subjectTo( AT_END , v == 0.0 ); 00070 00071 ocp.subjectTo( -0.01 <= v <= 1.3 ); 00072 00073 ocp.subjectTo( u*u >= -1.0 ); 00074 00075 00076 // DEFINE A PLOT WINDOW: 00077 // --------------------- 00078 GnuplotWindow window; 00079 window.addSubplot( s,"DifferentialState s" ); 00080 window.addSubplot( v,"DifferentialState v" ); 00081 window.addSubplot( m,"DifferentialState m" ); 00082 window.addSubplot( u,"Control u" ); 00083 window.addSubplot( PLOT_KKT_TOLERANCE,"KKT Tolerance" ); 00084 // window.addSubplot( 0.5 * m * v*v,"Kinetic Energy" ); 00085 00086 00087 // DEFINE AN OPTIMIZATION ALGORITHM AND SOLVE THE OCP: 00088 // --------------------------------------------------- 00089 OptimizationAlgorithm algorithm(ocp); 00090 00091 // algorithm.set( INTEGRATOR_TYPE, INT_BDF ); 00092 00093 // algorithm.set( INTEGRATOR_TOLERANCE, 1e-6 ); 00094 // algorithm.set( KKT_TOLERANCE, 1e-3 ); 00095 00096 //algorithm.set( DYNAMIC_SENSITIVITY, FORWARD_SENSITIVITY ); 00097 00098 00099 00100 algorithm.set( HESSIAN_APPROXIMATION, EXACT_HESSIAN ); 00101 algorithm.set( MAX_NUM_ITERATIONS, 20 ); 00102 algorithm.set( KKT_TOLERANCE, 1e-10 ); 00103 // algorithm.set( MAX_NUM_INTEGRATOR_STEPS, 4 ); 00104 00105 algorithm << window; 00106 algorithm.solve(); 00107 00108 // BlockMatrix sens; 00109 // algorithm.getSensitivitiesX( sens ); 00110 // sens.print(); 00111 00112 return 0; 00113 } 00114 /* <<< end tutorial code <<< */ 00115 00116 00117 00118 // algorithm.set( DISCRETIZATION_TYPE, MULTIPLE_SHOOTING ); 00119 // algorithm.set( DISCRETIZATION_TYPE, SINGLE_SHOOTING ); 00120 // 00121 // algorithm.set( DYNAMIC_SENSITIVITY, FORWARD_SENSITIVITY ); 00122 // algorithm.set( DYNAMIC_SENSITIVITY, BACKWARD_SENSITIVITY ); 00123 00124 // algorithm.set( INTEGRATOR_TYPE, INT_RK45 ); 00125 // algorithm.set( INTEGRATOR_TYPE, INT_RK78 ); 00126 // algorithm.set( INTEGRATOR_TYPE, INT_BDF ); 00127 // 00128 // algorithm.set( KKT_TOLERANCE, 1e-4 ); 00129 // algorithm.set( MAX_NUM_ITERATIONS, 20 ); 00130 00131 // algorithm.set( PRINT_SCP_METHOD_PROFILE, YES );