I have recently been looking into the use of the discrete associated Laguerre polynomials for the design of digital controllers/compensators, and flexible/configurable digital filters in general. I wouldn't say they are optimal, but they are certainly useful. You could probably use them to design an optimal controller if you wanted to.       

Dear Hugh Lachlan,

Its my pleasure to use the work you did that. would you please send me the utilized code. and if it is possible,  the explanation about your work to more understanding.

Thanks,

I uploaded this just then. It is a general overview of the (low-pass) filter design method - i.e polynomial regression analysis.

It does not specifically look at control but I have used them in that application (and lots of others). The ease with which the gain and phase profile can be arbitrarily manipulated does make them very useful in control.problems.

The use of discrete orthogonal polynomials is not really essential here but it does simplify filter analysis and realization, especially if you want to do extra processing, in addition to your smoothing (like variance analysis, change detection, classification, compression, etc). Because when you do the math, multiplications involving the basis- function matrices just vanish. Just like when orthogonal complex sinusoids are used as regressors in the DFT.   

Work with the Legendre polynomials for FIR filter design or the Laguerre polynomials for IIR filters. I generally prefer the latter.    

Research Generalized IIR Savitzky-Golay Filters: Derivation, Paramete...

thanks santos