ACADOintegrators is a collection of different integrators for solving ODE and
DAE systems including efficient sensitivity generation.
ACADOintegratorsSettings returns a settings struct for calling ACADOintegrators.
Call
settings = ACADOintegratorsSettings;
for obtaining a settings struct comprising the following items:
Model -- a) File name (without .cpp) containing the C++
implementation of the ODE/DAE,
e.g. 'gettting_started' for getting_started.cpp
b) a cell array of size one containing a Matlab
function handle to an ODE specified in an m-script,
e.g. '{ @glycemia_matlab }' for an ODE given as:
dx = glycemia_matlab( t,x,u,p,w )
c) a cell array of size one containing a Matlab
function handle to a DAE specified in an m-script,
e.g. '{ @simple_dae_matlab }' for an DAE given as:
f = glycemia_matlab( t,x,xa,u,p,w )
Integrator -- Name of one of the following integrators:
a) 'RK12' for an error-controlled Runge-Kunga12
b) 'RK23' for an error-controlled Runge-Kunga23
c) 'RK45' for an error-controlled Runge-Kunga45
d) 'RK78' for an error-controlled Runge-Kunga78
e) 'BDF' for an error-controlled, implicit integrator
based on the backward differentiation formula
Tolerance -- Integration tolerance
AbsoluteTolerance -- Integration absolute tolerance
MaxNumberOfSteps -- Maximum number of integrator steps
MinimumStepSize -- Minimum integrator step size
MaximumStepSize -- Maximum integrator step size
InitialStepSize -- Initial step size integrator
CorrectorTolerance -- Corrector Tollerance
StepSizeTuning -- Step size tuning parameter
LinearAlgebraSolver -- Specifies how the linear systems are solved:
a) 'dense' for a dense solver
b) 'sparse' for a sparse solver
u -- Constant value of controls affecting the ODE/DAE
p -- Constant value of parameters affecting the ODE/DAE
w -- Constant value of disturbances affecting the ODE/DAE
dxInit -- Initial value for differential states derivatives
(only for DAEs)
SensitivityMode -- String specifying one of the following modes for
efficient sensitivity generation:
a) '' (empty) for no sensitivity generation
b) 'AD_FORWARD' for 1st order forward sensitivities
c) 'AD_BACKWARD' for 1st order backward sensitivities
d) 'AD_FORWARD2' for 2nd order forward sensitivities
e) 'AD_FORWARD_BACKWARD' for 2st order sensitivities,
first forward then backward
mu -- Backward seed
lambdaX -- Forward seed w.r.t. differential states x
lambdaU -- Forward seed w.r.t. controls u
lambdaP -- Forward seed w.r.t. parameters p
lambdaW -- Forward seed w.r.t. disturbances w
mu2 -- Backward seed (2nd order)
lambdaX2 -- Forward seed w.r.t. differential states x (2nd order)
lambdaU2 -- Forward seed w.r.t. controls u (2nd order)
lambdaP2 -- Forward seed w.r.t. parameters p (2nd order)
lambdaW2 -- Forward seed w.r.t. disturbances w (2nd order)
PrintLevel -- Flag indicating if integrator shall print messages to
Matlab command window: 0 for no, 1 for yes
PlotXTrajectory -- Array containg a list of all indices of differential
states that shall be printed, e.g. [] for none
PlotXaTrajectory -- Array containg a list of all indices of algebraic
states that shall be plotted, e.g. [] for none
UseSubplots -- Flag indicating if plot routine shall use subplots in
order to use fewer figures: 0 for no, 1 for yes
StorageResolution -- Defines the number of time points at which the trajectory
is stored and optionally plotted. By default these time
points are equidistant and 101 in total.
Except for Model and Integrator, all components are optional and default
values might be used by the respective integrator. In particular, if
SensitivityMode is empty, no sensitivities are calculated and no seeds need
to be given (otherwise, at least on non-empty seed is expected).
As a short-cut, you can also call
settings = ACADOintegratorsSettings( 'modelname','integratorname' );
for obtaining a settings struct with Model set to 'modelname' and Integrator
set to 'integratorname' and all other components empty. This might be directly
used (inlined) within a call to ACADOintegrators.
See also ACADOINTEGRATORS, ACADOINTEGRATORSOUTPUTS
For additional information see the ACADOintegrators Tutorial and User's Manual
or visit http://www.acadotoolkit.org.
Please send remarks and questions to support@acadotoolkit.org!
Licence:
This file is part of ACADO Toolkit - (http://www.acadotoolkit.org/)
ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
Copyright (C) 2008-2009 by Boris Houska and Hans Joachim Ferreau, K.U.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
Author: Niels Haverbeke, Boris Houska, Hans Joachim Ferreau, David Ariens
Date: 2008-20100001 %ACADOintegrators is a collection of different integrators for solving ODE and 0002 %DAE systems including efficient sensitivity generation. 0003 %ACADOintegratorsSettings returns a settings struct for calling ACADOintegrators. 0004 % 0005 %Call 0006 % 0007 % settings = ACADOintegratorsSettings; 0008 % 0009 %for obtaining a settings struct comprising the following items: 0010 % 0011 % Model -- a) File name (without .cpp) containing the C++ 0012 % implementation of the ODE/DAE, 0013 % e.g. 'gettting_started' for getting_started.cpp 0014 % b) a cell array of size one containing a Matlab 0015 % function handle to an ODE specified in an m-script, 0016 % e.g. '{ @glycemia_matlab }' for an ODE given as: 0017 % dx = glycemia_matlab( t,x,u,p,w ) 0018 % c) a cell array of size one containing a Matlab 0019 % function handle to a DAE specified in an m-script, 0020 % e.g. '{ @simple_dae_matlab }' for an DAE given as: 0021 % f = glycemia_matlab( t,x,xa,u,p,w ) 0022 % 0023 % Integrator -- Name of one of the following integrators: 0024 % a) 'RK12' for an error-controlled Runge-Kunga12 0025 % b) 'RK23' for an error-controlled Runge-Kunga23 0026 % c) 'RK45' for an error-controlled Runge-Kunga45 0027 % d) 'RK78' for an error-controlled Runge-Kunga78 0028 % e) 'BDF' for an error-controlled, implicit integrator 0029 % based on the backward differentiation formula 0030 % 0031 % Tolerance -- Integration tolerance 0032 % AbsoluteTolerance -- Integration absolute tolerance 0033 % MaxNumberOfSteps -- Maximum number of integrator steps 0034 % MinimumStepSize -- Minimum integrator step size 0035 % MaximumStepSize -- Maximum integrator step size 0036 % InitialStepSize -- Initial step size integrator 0037 % CorrectorTolerance -- Corrector Tollerance 0038 % StepSizeTuning -- Step size tuning parameter 0039 % LinearAlgebraSolver -- Specifies how the linear systems are solved: 0040 % a) 'dense' for a dense solver 0041 % b) 'sparse' for a sparse solver 0042 % 0043 % u -- Constant value of controls affecting the ODE/DAE 0044 % p -- Constant value of parameters affecting the ODE/DAE 0045 % w -- Constant value of disturbances affecting the ODE/DAE 0046 % dxInit -- Initial value for differential states derivatives 0047 % (only for DAEs) 0048 % 0049 % SensitivityMode -- String specifying one of the following modes for 0050 % efficient sensitivity generation: 0051 % a) '' (empty) for no sensitivity generation 0052 % b) 'AD_FORWARD' for 1st order forward sensitivities 0053 % c) 'AD_BACKWARD' for 1st order backward sensitivities 0054 % d) 'AD_FORWARD2' for 2nd order forward sensitivities 0055 % e) 'AD_FORWARD_BACKWARD' for 2st order sensitivities, 0056 % first forward then backward 0057 % 0058 % mu -- Backward seed 0059 % lambdaX -- Forward seed w.r.t. differential states x 0060 % lambdaU -- Forward seed w.r.t. controls u 0061 % lambdaP -- Forward seed w.r.t. parameters p 0062 % lambdaW -- Forward seed w.r.t. disturbances w 0063 % mu2 -- Backward seed (2nd order) 0064 % lambdaX2 -- Forward seed w.r.t. differential states x (2nd order) 0065 % lambdaU2 -- Forward seed w.r.t. controls u (2nd order) 0066 % lambdaP2 -- Forward seed w.r.t. parameters p (2nd order) 0067 % lambdaW2 -- Forward seed w.r.t. disturbances w (2nd order) 0068 % 0069 % PrintLevel -- Flag indicating if integrator shall print messages to 0070 % Matlab command window: 0 for no, 1 for yes 0071 % PlotXTrajectory -- Array containg a list of all indices of differential 0072 % states that shall be printed, e.g. [] for none 0073 % PlotXaTrajectory -- Array containg a list of all indices of algebraic 0074 % states that shall be plotted, e.g. [] for none 0075 % UseSubplots -- Flag indicating if plot routine shall use subplots in 0076 % order to use fewer figures: 0 for no, 1 for yes 0077 % StorageResolution -- Defines the number of time points at which the trajectory 0078 % is stored and optionally plotted. By default these time 0079 % points are equidistant and 101 in total. 0080 % 0081 %Except for Model and Integrator, all components are optional and default 0082 %values might be used by the respective integrator. In particular, if 0083 %SensitivityMode is empty, no sensitivities are calculated and no seeds need 0084 %to be given (otherwise, at least on non-empty seed is expected). 0085 % 0086 %As a short-cut, you can also call 0087 % 0088 % settings = ACADOintegratorsSettings( 'modelname','integratorname' ); 0089 % 0090 %for obtaining a settings struct with Model set to 'modelname' and Integrator 0091 %set to 'integratorname' and all other components empty. This might be directly 0092 %used (inlined) within a call to ACADOintegrators. 0093 % 0094 % 0095 %See also ACADOINTEGRATORS, ACADOINTEGRATORSOUTPUTS 0096 % 0097 % 0098 %For additional information see the ACADOintegrators Tutorial and User's Manual 0099 %or visit http://www.acadotoolkit.org. 0100 % 0101 %Please send remarks and questions to support@acadotoolkit.org! 0102 % 0103 % Licence: 0104 % This file is part of ACADO Toolkit - (http://www.acadotoolkit.org/) 0105 % 0106 % ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization. 0107 % Copyright (C) 2008-2009 by Boris Houska and Hans Joachim Ferreau, K.U.Leuven. 0108 % Developed within the Optimization in Engineering Center (OPTEC) under 0109 % supervision of Moritz Diehl. All rights reserved. 0110 % 0111 % ACADO Toolkit is free software; you can redistribute it and/or 0112 % modify it under the terms of the GNU Lesser General Public 0113 % License as published by the Free Software Foundation; either 0114 % version 3 of the License, or (at your option) any later version. 0115 % 0116 % ACADO Toolkit is distributed in the hope that it will be useful, 0117 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0118 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0119 % Lesser General Public License for more details. 0120 % 0121 % You should have received a copy of the GNU Lesser General Public 0122 % License along with ACADO Toolkit; if not, write to the Free Software 0123 % Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 0124 % 0125 % Author: Niels Haverbeke, Boris Houska, Hans Joachim Ferreau, David Ariens 0126 % Date: 2008-2010 0127 0128 function [ settings ] = ACADOintegratorsSettings( model,integrator ) 0129 0130 settings = struct( 'Model',[],... 0131 'Integrator',[],... 0132 'Tolerance',[],... 0133 'AbsoluteTolerance',1e-6,... 0134 'MaxNumberOfSteps',1000,... 0135 'MinimumStepSize',1e-6,... 0136 'MaximumStepSize',1e8,... 0137 'InitialStepSize',1e-3,... 0138 'CorrectorTolerance', 1e-14,... 0139 'StepSizeTuning',0.5,... 0140 'LinearAlgebraSolver','dense',... 0141 'u',[],... 0142 'p',[],... 0143 'w',[],... 0144 'dxInit',[],... 0145 'SensitivityMode',[],... 0146 'mu',[],... 0147 'lambdaX',[],... 0148 'lambdaU',[],... 0149 'lambdaP',[],... 0150 'lambdaW',[],... 0151 'mu2',[],... 0152 'lambda2X',[],... 0153 'lambda2U',[],... 0154 'lambda2P',[],... 0155 'lambda2W',[],... 0156 'PrintLevel',1,... 0157 'PlotXTrajectory',[],... 0158 'PlotXaTrajectory',[],... 0159 'UseSubplots',0, ... 0160 'StorageResolution',101, ... 0161 'Jacobian', []); 0162 0163 switch ( nargin ) 0164 case 0 0165 return; 0166 0167 case 1 0168 settings.Model = model; 0169 return; 0170 0171 case 2 0172 settings.Model = model; 0173 settings.Integrator = integrator; 0174 settings.Tolerance = determineDefaultTolerance( integrator ); 0175 return; 0176 0177 otherwise 0178 disp('ERROR (integratorSettings): At most two input arguments allowed!'); 0179 return; 0180 end 0181 0182 end 0183 0184 0185 function [ tolerance ] = determineDefaultTolerance( integrator ) 0186 0187 switch ( integrator ) 0188 case 'BDF' 0189 tolerance = 1e-6; 0190 return; 0191 0192 case 'RK12' 0193 tolerance = 1e-1; 0194 return; 0195 0196 case 'RK23' 0197 tolerance = 1e-2; 0198 return; 0199 0200 case 'RK45' 0201 tolerance = 1e-6; 0202 return; 0203 0204 case 'RK78' 0205 tolerance = 1e-6; 0206 return; 0207 0208 otherwise 0209 tolerance = []; 0210 return; 0211 end 0212 0213 end