Progressive learning approach to stable adaptive control

In this paper, we present a novel approach to stable adaptive control of complex systems with high relative orders. In this approach, called “progressive learning”, we design a series of reference inputs that allow the system to learn parameters recursively 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