Progressive Learning: A New Approach to Stable Adaptive Control of High Relative-Degree Systems

Abstract

A novel approach to stable adaptive control of complex systems with high relative orders is presented. 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 those having a full spectrum. This progressive excitation method, termed “progressive learning,” allows for stable adaptive control even when a system’s relative order is three or higher. An averaging method is used to obtain stability conditions in terms of the 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 the adaptation by providing a series of reference inputs having appropriate frequency spectra. A numerical example is provided to verify the above analysis.