Fuller's Problem (optimica)

// Fuller's problem for an optimal chattering solution.
// (c) Sebastian Sager, 2005-2009
// More info on http://mintoc.de/index.php/Fuller's_Problem
 
package fuller_pack
 
  optimization fuller_opt (objective = cost(finalTime),
                         startTime = 0,
                         finalTime = 1)
 
    // Differential states
    Real x0(start=0.01);
    Real x1(start=0);
    Real cost(start=0);
 
    // The control signal
    input Real u(free=true);
 
  equation
    der(x0) = x1;
    der(x1) = 1-2*u;
    der(cost) = x0^2;
  constraint 
     u<=1;
     u>=0;
     x0(finalTime)=0.01;
     x1(finalTime)=0;
  end fuller_opt;
 
end fuller_pack;