New developments in progressive learning for stable adaptive control of high relative-degree systems

Abstract

New developments in progressive learning for stable adaptive control are presented. Progressive learning is a method that allows for stable adaptive control with a simple adaptation rule even when a system's relative order is three or higher. In the progressive learning method, a series of reference inputs are designed so that the system can learn control parameters stably and progressively, starting with the ones associated with low frequencies and moving up to the ones with a full spectrum. An averaging method is used to obtain stability conditions in terms of frequency contents of the reference inputs. Based on this analysis, we prove that the stable convergence of control parameters is guaranteed if the system is excited gradually in accordance with the progress of adaptation by providing a series of reference inputs having appropriate frequency spectra. A numerical example is provided to verify the above analysis.