MPC using casadi.Opti()

[JX Yu]

Hello everyone,

I use casadi.Opti() in matlab to solve quadratic form of MPC sum(x'Qx+u'*R*u) with input constraints in the control horizon is subject to -u_max<=u<=u_max. x is 4*1 and u is 1*1. p is the initial state of x.

I tried qpoases, nlpsol and qrqp. But simliar erros show that it cannot load shared library. I have already added casadi path to matlab. Do I need to download these solvers files?

opti=casadi.Opti();

Np=30;Nc=20;

x=opti.variable(4,Np);

u=opti.variable(1,Nc);

p=opti.parameter(4,1);

sumx=0;sumu=0;

for kp=1:Np-1

    if kp<=Nc

        opti.subject_to(x(:,kp+1)==AT*x(:,kp)+B2*u(1,kp)+D0);

        sumu=u(1,kp)'*R*u(1,kp)+sumu;

    else

        opti.subject_to(x(:,kp+1)==AT*x(:,kp)+B2*u(1,Nc)+D0);

    end

    sumx=sumx+x(:,kp+1)'*Q*x(:,kp+1);

end

opti.subject_to(norm(u,inf)<=u_max);

sum=sumx+sumu;

opti.subject_to(x(:,1)==p);

opti.set_value(p,[ey;vy+vx*ephi;ephi;yawrate-vx*rho]);

opti.minimize(sum);

opti.solver('nlpsol');

sol=opti.solve();

CasADi -  WARNING(".../casadi/core/plugin_interface.hpp:322: Assertion "handle!=nullptr" failed:

PluginInterface::load_plugin: Cannot load shared library 'libcasadi_nlpsol_nlpsol.dll': 

   (

    Searched directories: 1. casadipath from GlobalOptions

                          2. CASADIPATH env var

                          3. PATH env var (Windows)

                          4. LD_LIBRARY_PATH env var (Linux)

                          5. DYLD_LIBRARY_PATH env var (osx)

    A library may be 'not found' even if the file exists:

          * library is not compatible (different compiler/bitness)

          * the dependencies are not found

   )

  Tried 'E:\casadi-windows-matlabR2016a-v3.5.1' :

    Error code (WIN32): 126

  Tried '' :

    Error code (WIN32): 126

  Tried '.' :

    Error code (WIN32): 126") [.../casadi/core/plugin_interface.hpp:171]

Error using casadi.Opti/solve (line 253)

Error in Opti::solve [OptiNode] at .../casadi/core/optistack.cpp:159:

.../casadi/core/plugin_interface.hpp:417: Plugin 'nlpsol' is not found.

[Joris Gillis]

Hi there.

For conic problems, you need to initialize Opti with 'conic' argument:

opti=casadi.Opti('conic');
x=opti.variable(2);

opti.subject_to([1 2]*x<=-2);
opti.minimize(sumsqr(x));
opti.solver('qpoases');
sol=opti.solve();

sol.value(x)

Note that the norm(u,inf) formulation will not give satisfactory results.

Change to the equivalent:

opti.subject_to(u<=u_max);

Best regards,

  Joris

[JX Yu]

Hi Gillis,

Thanks for your reply. It works, But the solution is much different from other solver, "cvxgen" while I guess my code is right.

And could I speed up the solver to 0.01s while it takes 0.13s to obtain a solution now?

Best,

Jiaxing