Why " The boundary condition function BCFUN should return a column vector of length 5" error message is came?
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% function Y6
solinit = bvpinit(linspace(0,1),[0;3;1;1],2);
sol = bvp4c(@ode, @bc, solinit);
y = sol.y;
time = sol.parameters*sol.x;
ut = -y(4,:);
figure(1);
plot(time,y([1 2],:)','-'); hold on;
plot(time, ut, 'k:');
axis([0 time(1,end) -1.5 3]);
text(1.3,2.5,'x_1(t)');
text(1.3,.9,'x_2(t)');
text(1.3,-.5,'u(t)');
xlabel('time');
ylabel('states');
title('Numerical solution');
hold off;
% -------------------------------------------------------------------------
% ODE's of augmented states
function dydt = ode(t,y,T)
dydt = T*[2*y(2);4*y(4);0;-2*y(3)];
end
% -------------------------------------------------------------------------
% boundary conditions: x1(0)=11;p2(0)=2; x2(tf)=3; 3*p1(tf)+p2(2)^2=0
function res = bc(ya,yb,T)
res = [ ya(1) - 11; ya(4); yb(2) - 3; 3*yb(3)+yb(4)^2];
end
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Réponse acceptée
Jan
le 14 Nov 2022
You provide an extra parameter:
solinit = bvpinit(linspace(0,1),[0;3;1;1],2);
% ^ here
But there is no condition for this parameter in bc().
4 commentaires
Jan
le 16 Nov 2022
This not trivial. If you do not know, which function u is, there is an infinite number of possible solutions. This is an optimization problem and not a simple BVP.
Plus de réponses (1)
Torsten
le 16 Nov 2022
Modifié(e) : Torsten
le 16 Nov 2022
Choose a grid
0=t0 < t1 < ... < tn = tf
With each grid point, associate a value ui of your control function u (the ui are your solution variables for the optimization problem).
Call fmincon with initial values for the ui.
Within the objective function for fmincon, solve the boundary value problem from above with the given vector u (e.g. using bvp4c or your own ODE solver for this simple boundary value problem) and return the value for J to the optimizer. The integral can be approximated by the trapezoidal rule, e.g.
Maybe the YouTube video is of help:
3 commentaires
Torsten
le 16 Nov 2022
I described the steps you have to follow and even gave a link to a video where everything is described in detail. This is all I can do for you - the task is not a "one-liner".
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