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
0 件のコメント
採用された回答
Jan
2022 年 11 月 14 日
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 件のコメント
Jan
2022 年 11 月 16 日
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.
その他の回答 (1 件)
Torsten
2022 年 11 月 16 日
編集済み: Torsten
2022 年 11 月 16 日
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 件のコメント
Torsten
2022 年 11 月 16 日
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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