Limiting the fit range is not possible. You could modify the function using the ternary operator (e.g. 'a>2?a:1e300'), but there is a high possibility that your fit becomes unstable, and it is really bad style. ;)
Try to predict your parameters as well as possible to keep them from straying in forbidden regions. Fit the parameters seperately in the beginning, e.g. introduce one of them in a simpler function, only use a small part of the data where part of the parameters is irrelevant, etc. Only in the last step fit your full function with all parameters and the whole dataset.
And gnuplot does have do for [] {} and while () {} loops that you can use to iterate over your dataset. Before you ask: Array variables to save the fit parameters were only recently intruduced in the development version 5.1.
Hi Karl Really thanks for this hint. I had a hard time trying to find a proper way to do this. I am gonna proceed and try it out. Sincerely !!