Estimating Relative Degree of Nonlinear Systems Using Generating Series.

The notion of relative degree plays a central role in a number of feedback control design techniques for nonlinear systems. But there appears to be no existing general method for identifying relative degree from data beyond techniques best suited for sliding mode control. The goal of this paper is to present a method for identifying the relative degree of any single-input, single-output nonlinear system whose Chen-Fliess functional series representation has a well defined relative degree. Specifically, a three step algorithm is developed to estimate the relative degree from a noisy estimate of its generating series. The method is demonstrated using a three species Lotka-Volterra system.