This is a prime candidate for "grey box" modeling with the "System Identification Toolbox" which has a nice GUI.
If you want to use fmincon use the following:
ab0 = [1; 1]; % initial guess
A = [ 1 0; % a<100
-1 0; % a>0
0 1; % b<22
0 -1];% b>0
b = [100*(1-eps); % a<100
0-eps; % a>0
22*(1-eps); % b<22
0-eps]; % b>0
ab = fimcon(@sumOfThem, ab0, A, b);
a = ab(1);
b = ab(2);
