CasADi

import casadi.*


x = MX.sym('x',2); % Two states
p = MX.sym('p');   % Free parameter

% Expression for ODE right-hand side
z = 1-x(2)^2;
rhs = [z*x(1)-x(2)+2*tanh(p);x(1)];

% ODE declaration with free parameter
ode = struct('x',x,'p',p,'ode',rhs);

% Construct a Function that integrates over 1s
F = integrator('F','cvodes',ode,0,1);

% Control vector
u = MX.sym('u',5,1);

x = [0;1]; % Initial state
for k=1:5
  % Integrate 1s forward in time:
  % call integrator symbolically
  res = F('x0',x,'p',u(k));
  x = res.xf;
end

% NLP declaration
nlp = struct('x',u,'f',dot(u,u),'g',x);

% Solve using IPOPT
solver = nlpsol('solver','ipopt',nlp);
res = solver('x0',0.2,'lbg',0,'ubg',0);

plot(full(res.x))

from casadi import *
from matplotlib.pyplot import plot, show

x = MX.sym('x',2)  # Two states
p = MX.sym('p')    # Free parameter

# Expression for ODE right-hand side
z = 1-x[1]**2;
rhs = vertcat(z*x[0]-x[1]+2*tanh(p),x[0])

# ODE declaration with free parameter
ode = {'x':x,'p':p,'ode':rhs}

# Construct a Function that integrates over 1s
F = integrator('F','cvodes',ode,0,1)

# Control vector
u = MX.sym('u',4,1)

x = [0,1]  # Initial state
for k in range(4):
  # Integrate 1s forward in time:
  # call integrator symbolically
  res = F(x0=x,p=u[k])
  x = res['xf']


# NLP declaration
nlp = {'x':u,'f':dot(u,u),'g':x}

# Solve using IPOPT
solver = nlpsol('solver','ipopt',nlp)
res = solver(x0=0.2,lbg=0,ubg=0)

plot(res['x'])
show()

#include <casadi/casadi.hpp>
using namespace casadi;

MX x = MX::sym("x",2); // Two states
MX p = MX::sym("p");   // Free parameter

// Expression for ODE right-hand side
MX z = 1-pow(x(1),2);
MX rhs = vertcat(z*x(0)-x(1)+2*tanh(p),x(0));

// ODE declaration with free parameter
MXDict ode = {{"x",x},{"p",p},{"ode",rhs}};

// Construct a Function that integrates over 1s
Function F = integrator("F","cvodes",ode,0,1);

// Control vector
MX u = MX::sym("u",4,1);

x = DM(std::vector<double>{0,1});  // Initial state
for (int k=0;k<4;++k) {
  // Integrate 1s forward in time:
  // call integrator symbolically
  MXDict res = F({{"x0",x},{"p",u(k)}});
  x = res["xf"];
}

// NLP declaration
MXDict nlp = {{"x",u},{"f",dot(u,u)},{"g",x}};

// Solve using IPOPT
Function solver = nlpsol("solver","ipopt",nlp);
DMDict res = solver(DMDict{{"x0",0.2},{"lbg",0},{"ubg",0}});