Is there a mat apparatus for constructing a linear interpolation with moving ends?

Question

Mathematics

Good afternoon! There is a function graph describing a certain process. There is a linear regulator. By taking several points of the graph, using linear interpolation, you can get a graph of the regulator. But there is one problem ... On the process graph there are permissible errors that cannot be exceeded, the graph is roughly "hyperbole". Accordingly, in the places of inflection, the straight line connecting the two points goes beyond the range. The solution, obviously, is to adjust the value of the interpolation nodes (the value of x and y) so that the resulting straight line does not go beyond the allowable values. Is there any approach to solve this problem? Thanks

Answer 1

Read TAU - the theory of automatic control.