Progressive Learning: Part I — Stability Analysis

This paper presents a new input design method for stable adaptive control of complex systems with high relative orders. This method, called “progressive learning,” allows 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. We apply a method of averaging analysis to obtain stability conditions in terms of frequency contents of the reference input. 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.