The work presented here exploits elimination theory (solving systems of polynomial equations in several variables)  to perform nonlinear parameter identification. In particular show how this technique can be used to estimate the rotor time constant and the stator resistance values of an induction machine. Although the example here is restricted to an induction machine, parameter estimation is applicable to many practical engineering problems. In , L. Ljung has outlined many of the challenges of nonlinear system identification as well as its particular importance for biological systems. In these types of problems, the model developed for analysis is typically a nonlinear state space model with unknown parameter values. The typical situation is that only a few of the state variables are measurable requiring that the system be reformulated as a nonlinear input-output model. In turn, resulting the nonlinear input-output model is almost always nonlinear in the parameters. Towards that end, differential algebra tools for analysis of nonlinear systems have been developed by Michel Fliess  and Diop . Moreover, Ollivier  as well as Ljung and Glad  have developed the use of the characteristic set of an ideal as a tool for identification problems. The use of these differential algebraic methods for system identification have also been considered in , . The focus of their research has been the determination of a priori identifiability of a given system model. However, as stated in , the development of an efficient algorithm using these differential algebraic techniques is still unknown. Here, in contrast, a method for which one can actually numerically obtain the numerical value of the parameters is presented. We also point out that  has also done work applying elimination theory to systems problems.
Chiasson, John and Oteafy, Ahmed. (2011). "Elimination Theory for Nonlinear Parameter Estimation". Lecture Notes in Control and Information Sciences, 407/201165-75. http://dx.doi.org/10.1007/978-3-642-16135-3_6