Algebraic Methods for Function Reconstruction: Application to System Identification

We consider functions that have a known structure but involve a number of unknown parameters. Specifically, we consider classes of functions that involve sums of exponential terms. The values of the function and some of its derivatives are given at a finite number of points and it is of interest to uniquely reconstruct the function from the given data. In this paper we consider this problem and suggest algebraic methods of solution. We also show how these methods can be used as the basis of algorithms for system identification. The methods are simple, mathematically rigorous and analytical in nature. In the case of low order systems they can be very easily presented and executed. These attributes make the techniques very appealing for introductory treatments of the subject matter for students in systems and control