Least-Squares Parameter Identification

Abstract

This chapter presents the fundamental theory of least-squares parameter identification. Least-squares methods are central to function approximation theory and data regression analysis. Least-squares methods can also be used in adaptive control as indirect adaptive control methods to estimate unknown system parameters to provide the information for adjusting the control gains. The batch least-squares method is often used for data regression analysis. Least-squares gradient and recursive least-squares methods are well-suited for on-line time series analysis and adaptive control. The concept of persistent excitation is introduced as a fundamental requirement for exponential parameter convergence of least-squares methods. Indirect least-squares adaptive control theory is introduced. The adaptation signal is based on the plant modeling error in contrast to the tracking error for model-reference adaptive control. An important notion to recognize is that the plant modeling error is the source of the tracking error and not vice versa. The combined least-squares model-reference adaptive control uses both the plant modeling error and tracking error for adaptation. As a result, the adaptation mechanism is highly effective. Both the least-squares gradient and recursive least-squares methods can also be used separately in adaptive control without combining with model-reference adaptive control. A fundamental difference with the least-squares adaptive control methods from model-reference adaptive control is that a parameter convergence to true system parameters is guaranteed in the presence of a persistently exciting input signal.