How to make a polyfit with constraints to the first and second derivative?

I want to make a polyfit of some data. The start and end point, and also the derivative and second derivative in begin and endpoint are knowns, how do I make a polyfit, which fulfills to this needs?

I found a polyfix, function, where you can give constraints to the start and end point, and also the derivative, but you cannot add a constraint to the second derivative. Is there another solution?

This is the link to the polyfix function: https://nl.mathworks.com/matlabcentral/fileexchange/54207-polyfix-x-y-n-xfix-yfix-xder-dydx

Answer 1

[Matt J]

More often than not, if you have such constraints, it is spline that you want to fit, not a polynomial. Constrained spline fits can be done with this FEX download:

https://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

[Toon Van Dyck]

I already tried the slm function. I need a polynomial function of at least degree 5, and this function can only fit functions of degrees 1,2 and 4.

[Matt J]

Yes, but they are splines. An order 4 spline is much more flexible than a degree five polynomial.

Answer 2

[Matt J]

Well they are just linear constraints on the coefficients, so you could use lsqlin if you have the Optimization Toolbox.