I am currently studying a problem in which I am required to predict a response from a set data obtained from an electrical instrument from a set of data. I am looking for any advice on the best algorithm(s) to use to generate a best curve of the given data set. However the curve must statify several criteria:
1) The curve must have be smooth.
2) The curve below a certain is linear above this point the curve asymtotes parallel to the y-curve axis.
3) The two curves (I think this is only way to achieve the above criteria point) needs to transition 'seemlessly' with little or no change in gradient between the two.
4) The gradient of the curve above the set point should be constant and increasing.
5) The curve must go through the last point in the data set.
I have looked at most the usual options for modelling this but cannot find one that statifys all the above points, so would be grateful if anyone could point me in the right direction and let me know of any know pitfalls the suggested algorithm might have.