DGM(2,1)模型
clc,clear;
x0=[2.874 3.278 3.39 3.679 3.77 3.8];
n=length(x0);
a_x0=diff(x0)';
B=[-x0(2:end)',ones(n-1,1)];
u=B\a_x0syms x(t)
d2x=diff(x,2);dx=diff(x);x=dsolve(d2x+u(1)*dx==u(2),x(0)==x0(1),dx(0)==x0(1));
xt=vpa(x,6)
yuce=subs(x,t,[0:n-1]);
yuce=double(yuce)
x0_hat=[yuce(1),diff(yuce)]
epsilon=x0-x0_hat;
delta=abs(epsilon./x0)
result
u =
0.4241.7046
xt =
4.0202t + 2.70331exp(-0.423997*t) + 0.170692
yuce =
2.874 5.96 9.3688 12.989 16.747 20.596
x0_hat =
2.874 3.086 3.4088 3.6201 3.7584 3.8488
delta =
0 0.058572 0.005556 0.016008 0.0030859 0.012855