Minimizing ODE parameter with Experimental Data

I am trying to minimize these two functions: and using specific literature data. I have tried a couple of different ways, but nothing seems to be working. The parameters and are the parameters I am wanting to minimize. Any suggestions?

[Walter Roberson]

What is the form of the known data?

Is this perhaps a boundary value problem?

[Natalie Bell]

Potentially a boundary value but there are four unknowns.

This is the data I have in matlab:

t=[1:1:27];
y=[4.91,39.64,32.82,17.43,17.58,9.01,6.63,32.00,13.44,11.69,15.65,16.76,15.96,13.73,33.87,19.75,21.97,26.56,20.06,32.11,20.05,17.67,14.65,7.02,4.63,6.21,6.03];