On Identification of Non-linear Regression Models: Application to the Pole-Zero Cancellation Problem in Adaptive Control

摘要

In this paper, we are interested in the problem of estimation of non-linearly parametrised regression models of the form y = f(θ_*)~Tφ. First, we recall that a 'classical' gradient search, where the gradient is evaluated in the parameter space, is globally convergent if f(θ_*)~Tφ is convex in θ. Then, we show how this condition can be removed if we instead evaluate the gradient in the f space. To the best of our knowledge, in spite of its remarkable simplicity, this idea has not been reported in the literature.