Here is a sample solution. It uses calcZ(), which I posted previously, and it uses the simulated data file which I posted previously. The main program is fitKKJ.m. It calls fmincon() and it passes function sseZY() to fmincon(). Function sseZY is attached. There are comments in fitKKJ.m and in sseZY.m which explain how each works.
Here is the console output when I run the script:
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
Best fit values: a=0.771, x=0.047.
The simulated data (ten y,z pairs) was generated with a=1, x=0, and Gaussian noise was added.
The script also plots the measured (or simulated, in this case) data and the best-fit approximation. See plot below.