How to Extrapolate a 1D Chirped Signal?

Following a past question, I’d like to extrapolate a signal like the one below: (red is signal, blue is the the extrapolated )

t1 = 0:0.1:30;
t2 = 0:0.1:40;
s = @(t) sin(0.2*t)+sin(0.5*t+0.05*t.^2); 
figure;
plot(t2,s(t2)); hold on
plot(t1,s(t1));

Linear predictive coding, or AR Burg’s method are not successful here.
How can you extrapolate that?