Error: The integration routine stopped as the required accuracy can not be obtained

[Derek Biega]

I am using the ACADO toolkit to minimize the time for a small aircraft to go from takeoff to cruise. I have 4 differential states: velocity, range, height, and flight path angle, and 1 control: u. When I run the code, I get an error:

[ACADO] Error: The integration routine stopped as the required accuracy can not be obtained
Code: (RET_UNSUCCESSFUL_RETURN_FROM_INTEGRATOR_RK45)

Consequently, I also get several other errors stating that the NLP Solver Fails, and that the initialization of the optimization algorithm failed. I'm not exactly sure what I am doing wrong that the algorithm is not working. This is my first time using ACADO, and I am struggling to find good resources. Code below:

BEGIN_ACADO;                                % Always start with "BEGIN_ACADO".

    acadoSet('problemname', 'stackOverflow');

    DifferentialState v;                    % Velocity [m/s]
    DifferentialState r;                    % Range [m]
    DifferentialState h;                    % Height [m]
    DifferentialState gamma;                % Flight Path Angle [deg]
    Parameter T;                            % Minimize Time
    Control u;                              % Control input = Pitch angle

    alpha = minus(u,gamma);            % Angle of attack [deg]
    thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2);   % Thrust [N]
    m = double(4.2);                  % mass [kg]
    g = double(9.81);                 % gravity [m/s^2]

    %% Diferential Equation
    f = acado.DifferentialEquation(0, T);   % Set the differential equation object

    % Write down the ODE
    f.add(dot(v) == (1/m)*(thrust*cos(alpha)-thrust-(m*g*sin(gamma))));
    f.add(dot(r) == v*cos(gamma));                   
    f.add(dot(h) == v*sin(gamma));            
    f.add(dot(gamma) == 1/(m*v)*(thrust*sin(alpha)-thrust-m*g*sin(gamma)));

    %% Optimal Control Problem
    ocp = acado.OCP(0.0, T);                % Set up the Optimal Control Problem (OCP)                                    
    ocp.minimizeMayerTerm(T);               % Minimize the consumed energy
    ocp.subjectTo( f );                     % Optimize w.r.t your differential equation

    ocp.subjectTo( 'AT_START', r ==  0.0 );  % r(0) = 0
    ocp.subjectTo( 'AT_START', v ==  0.0 );  % v(0) = 0
    ocp.subjectTo( 'AT_START', h ==  10.0 ); % h(0) = 1
    ocp.subjectTo( 'AT_START', gamma ==  0.0 ); % gamma(0) = 1

    ocp.subjectTo( 'AT_END'  , h == 61.0 ); % h(T) = Cruise Altitude
    ocp.subjectTo( 'AT_END'  , v == 24.0 ); % v(T) = Cruise Velocity
    ocp.subjectTo( 'AT_END'  , gamma == 0.0 ); % gamma(T) = Cruise Flight Angle

    ocp.subjectTo( 14.013 <= v <= 27.0 );       % path constraint on speed
    ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb
    ocp.subjectTo( 3 <= alpha <= 3.3 );     % Possible cruise windows for stability


    %% Optimization Algorithm
    algo =acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP
    algo.set( 'KKT_TOLERANCE', 1e-8 );     % Set a custom KKT tolerance

END_ACADO;

% Run the test
out = stackOverflow_RUN();

[Derek Biega]

To add to this post, the cost function I am trying to solve is below. I suspect that I am using the incorrect method to solve this, as there is nowhere to define the weighted matrices, but I still do not understand why my program is failing. The insert image functionality does not seem to work in these forums, so the imgur link below is a way to see the cost function.
https://imgur.com/a/wAJAm89

[Derek Biega]

I've also tried implementing this function using LSQ, and am receiving the exact same error. I have no idea what could be wrong. here is that altered code:

clear; clc; close all;

BEGIN_ACADO;                                % Always start with "BEGIN_ACADO". 

    acadoSet('problemname', 'stackOverflow');

    DifferentialState v;                    % Velocity [m/s]
    DifferentialState r;                    % Range [m]
    DifferentialState h;                    % Height [m]
    DifferentialState gamma;                % Flight Path Angle [deg]

    Parameter T;                            % We would like to minize the T, so T is a parameter

    Control u;                              % Control input = Pitch angle [deg]

    alpha = minus(u,gamma);            % Angle of attack [deg] ( will be constrained)
    thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2);   % Thrust [N]
    m = 4.2;                  % mass [kg]
    g = 9.81;                 % gravity [m/s^2]

    %% Diferential Equation
    f = acado.DifferentialEquation(0, T);   % Set the differential equation object. We would like to minize the time.
    f.linkMatlabODE('ode');             % Link to a Matlab ODE

    %% Optimal Control Problem
    ocp = acado.OCP(0.0, T, 50);    % Set up the Optimal Control Problem (OCP)
                                    % Start at 0, go to T, 50 intervals

    Q = [.01 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0];
    obj = {v, r, h, gamma};                     % the LSQ-Function
    R = zeros(1,4);                         % The reference

    ocp.minimizeLSQ( Q, obj, R );             % Minimize this Least Squares Term
    ocp.subjectTo( f );                     % Optimize with respect to your differential equation

    ocp.subjectTo( 'AT_START', r ==  0.0 );  % r(0) = 0
    ocp.subjectTo( 'AT_START', v ==  0.0 );  % v(0) = 0
    ocp.subjectTo( 'AT_START', h ==  10.0 ); % h(0) = 1
    ocp.subjectTo( 'AT_START', gamma ==  0.0 ); % gamma(0) = 1

    ocp.subjectTo( 'AT_END'  , h == 61.0 ); % h(T) = Cruise Altitude
    ocp.subjectTo( 'AT_END'  , v == 24.0 ); % v(T) = Cruise Velocity
    ocp.subjectTo( 'AT_END'  , gamma == 0.0 ); % gamma(T) = Cruise Flight (Should be 0 at cruise)

    ocp.subjectTo( 14.013 <= v <= 27.0 );       % path constraint on speed
    ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb
    ocp.subjectTo( 3 <= alpha <= 3.3 );     % Possible cruise windows for stability


    %% Optimization Algorithm
    algo = acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP
    algo.set( 'INTEGRATOR_TOLERANCE', 1e-8 );     % Set a custom KKT tolerance
    algo.set( 'KKT_TOLERANCE', 1e-4 );     % Set a custom KKT tolerance

END_ACADO;     

% Run the test
out = stackOverflowTest_RUN();    

Full error output:
[ACADO] Error: The integration routine stopped as the required accuracy can not be obtained
Code: (RET_UNSUCCESSFUL_RETURN_FROM_INTEGRATOR_RK45)
File: C:\Users\djbie\ACADOtoolkit\acado\integrator\integrator_runge_kutta.cpp
Line: 1394

[ACADO] Error: Initialization of NLP solver failed
Code: (RET_UNABLE_TO_INTEGRATE_SYSTEM)
File: C:\Users\djbie\ACADOtoolkit\acado\dynamic_discretization\shooting_method.cpp
Line: 279

[ACADO] Error: Initialization of NLP solver failed
Code: (RET_NLP_INIT_FAILED)
File: C:\Users\djbie\ACADOtoolkit\acado\nlp_solver\scp_method.cpp
Line: 217

[ACADO] Error: Initialization of optimization algorithm failed
Code: (RET_OPTALG_INIT_FAILED)
File: C:\Users\djbie\ACADOtoolkit\acado\optimization_algorithm\optimization_algorithm_base.cpp
Line: 587

[Derek Biega]

Update:

So I've found out that this error is being triggered due to the values I select for my constraints. However, I do not understand why my selected values are flagging the system as such.

[Imane]

Hi,

I actually receive the same errors as you. I don't know if you figured it out.

Thank you!

[Youssef Elshebani]

Hi,

three years later and now I am gettting this since no one answered its hopeless outhere

[Imane]

Thank you for your response

Le jeu. 21 juil. 2022 à 21:07, Youssef Elshebani youssef93@users.sourceforge.net a écrit :

Hi,

three years later and now I am gettting this since no one answered its
hopeless outhere

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Error: The integration routine stopped as the required accuracy can not be
obtained
https://sourceforge.net/p/acado/discussion/general/thread/0aef41d16a/?limit=25#b8cd

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