Problem compiling tutorial: Optimal Control of Hybrid- and Multi-Stage Processes

[urs]

Hi,
In the tutorial “Optimal Control of Hybrid- and Multi-Stage Processes”, I have a problem getting the example code to compile.
The lines:

ocp.subjectTo( f1, 20 );
ocp.subjectTo( j      );
ocp.subjectTo( f2, 20 );

each generate the error, that no corresponding function call exists.
e.g for lines 1 and 3: no matching function for call to ‘ACADO::OCP::subjectTo(ACADO::DifferentialEquation&, int)’. I also can’t find the function calls in the online documentation.

Were they replaced by other functions, or what am I missing?

Thank you in advance.

[Boris]

Hi,

Thanks for posting this problem. Actually, the functionality
you are referring to got deprecated in the meanwhile---unfortunately,
the web-tutorial seems to be not updated yet.

The correct way to setup a multi-stage process is to define
new states/controls for each stage (you may even have different
numbers states on the stages) and re-scale all stage duration
to [0,T] (such that all have equal length). Then you can
simply stack everything into one ODE and formulate the
transition/jump conditions in form of coupled boundary value
constraints.

Best,
Boris

[Davide]

Hi!

A couple of questions about the setup of a multi-stage process:

1. Is it possible, in some way, to setup the problem in order to have a different duration for the two phases?
2. Is it possible to have a small example of how to correctly implement a problem like this? I tried to do so by following your advice but didn't manage to get a working piece of code (I have just begun learning ACADO, so I am not very confident about what I am doing :) ).
   Thanks!

[dmitry luchinsky]

Hi, has anyone working example with setting up multi-stage problem in acado? Thank you in davance, Dmitry

[Piche Elodie]

Hi,
I worked in the jo-jo example of ACADO that seems not to work. I found a solution to implement Multi-stage. Here is the piece of code that runs and gives the good results. As I red in the forum, I have defined new states for each phase.

int main( )
{
USING_NAMESPACE_ACADO

// THE VARIABLES OF THE JOJO:
// --------------------------
DifferentialState          x1;   // the position of the "hand"
DifferentialState          v1;   // the velocity of the "hand"
DifferentialState          y1;   // the position of the jojo
DifferentialState          w1;   // the velocity of the jojo

Control                    u1;   // the control action of the "hand"

DifferentialState          x2;   // the position of the "hand"
DifferentialState          v2;   // the velocity of the "hand"
DifferentialState          y2;   // the position of the jojo
DifferentialState          w2;   // the velocity of the jojo

Control                    u2;   // the control action of the "hand"

Parameter                 T1;   // the duration of phase I
Parameter                 T2;   // the duration of phase II


// THE GIVEN JOJO PARAMETERS:
// --------------------------
const double       m = 0.200;   // the mass of the jojo (200g)
const double       J = 1e-4 ;   // the inertia of the jojo (1e-4kg*m^2)
const double       r = 0.010;   // the coiling radius of the jojo (1cm)
const double       g = 9.81 ;   // the gravitational constant (9.81m/s^2)
const double       a = 1e-2 ;   // the coiling friction (1e-2/s)
const double       L = 1.00 ;   // the length of the rope (1m)


// OTHER USEFUL CONSTANTS:
// ---------------------------
const double k  = J/(m*r*r+J);   // the jojo's damping ratio
const double mu = 1.0 - k    ;   // the effective mass ratio


// THE MODEL EQUATIONS FOR PHASE I and II :
// ----------------------------------------
DifferentialEquation f1;                           // with normalized time
(f1 << dot(x1)) ==  v1*T1                   ;
(f1 << dot(v1)) ==  u1*T1                   ;
(f1 << dot(y1)) ==  w1*T1                   ;
 (f1 << dot(w1)) == (-mu*g + k*u1 + a*(v1-w1))  *T1;
(f1 << dot(x2)) ==  v2*T2                   ;
(f1 << dot(v2)) ==  u2*T2                   ;
(f1 << dot(y2)) ==  w2*T2                   ;
(f1 << dot(w2)) == (-mu*g + k*u2 + a*(v2-w2))  *T2;




// THE EQUATIONS FOR THE JUMP:
// ---------------------------

IntermediateState z1, a1, a2;


z1 = k*v1;
a1 = (z1 + sqrt( z1*z1 + k*(w1*w1-2.0*w1*v1))) ;
a2 = (x2-y2);


// DEFINE AN OPTIMAL CONTROL PROBLEM:
// ----------------------------------
OCP ocp1(0.0,1.0,20);
ocp1.minimizeLagrangeTerm( u1*u1*T1+ u2*u2*T2 );
ocp1.subjectTo(f1);

ocp1.subjectTo( AT_START     , x1   ==  0.00 );
ocp1.subjectTo( AT_START     , v1   ==  0.00 );
ocp1.subjectTo( AT_START     , y1   ==  0.00 );
ocp1.subjectTo( AT_START     , w1   ==  0.00 );

ocp1.subjectTo( AT_END     , x1-y1   ==  L );
ocp1.subjectTo( AT_END       , x2   == -0.10 );
ocp1.subjectTo( AT_END       , v2   ==  0.00 );
ocp1.subjectTo( AT_END       , a2   ==  0.00 );
ocp1.subjectTo( AT_END       , w2   ==  0.00 );


//PERIODIC BOUNDARY CONSTRAINTS:
// ----------------------------

ocp1.subjectTo(0.0, x2, -x1, 0.0);
ocp1.subjectTo(0.0, v2, -v1, 0.0);
ocp1.subjectTo(0.0, y2, -y1, 0.0);
ocp1.subjectTo(0.0, w2, -a1, 0.0);


ocp1.subjectTo( -10 <= u1 <= 10);
ocp1.subjectTo( -10 <= u2 <= 10);

ocp1.subjectTo( 0.1 <= T1 <= 2.0 );
ocp1.subjectTo( 0.1 <= T2 <= 4.0 );

// DEFINE AN OPTIMIZATION ALGORITHM AND SOLVE THE OCP:
// ---------------------------------------------------
OptimizationAlgorithm algorithm(ocp1);
algorithm.set(INTEGRATOR_TYPE, INT_RK45);
algorithm.set(DISCRETIZATION_TYPE,  MULTIPLE_SHOOTING );
algorithm.set(KKT_TOLERANCE, 1e-10);
algorithm.set(INTEGRATOR_TOLERANCE, 1e-8);
algorithm.set(MAX_NUM_ITERATIONS, 1000);
algorithm << window;
//algorithm.set( PRINT_SCP_METHOD_PROFILE, YES );
algorithm.solve();

VariablesGrid out_states;
VariablesGrid out_controls;
algorithm.getDifferentialStates(out_states);
algorithm.getControls(out_controls);
algorithm.getParameters("/home/laboratoire/mnt/E/Bureau/ElodieP/GIT_Vrille_ACADO/jojo_parameters.txt");

out_controls.appendValues(out_states);
out_controls.print("/home/laboratoire/mnt/E/Bureau/ElodieP/GIT_Vrille_ACADO/out_controls_norm.txt", "", PS_PLAIN);

// out_states.print("/home/laboratoire/mnt/E/Bureau/ElodieP/GIT_Vrille_ACADO/out_states_norm.txt", "", PS_PLAIN);

return 0;

}

Hope it will help !