Combined Direct and Indirect Approach to Adaptive Control

This note introduces a new approach to adaptive control using a combination of both direct and indirect methods. Based on the estimates of the plant parameters and the current values of the control parameters, closed-loop estimation errors εθ(t) and εk(t) are defined. These in turn are used in the adaptive laws for updating both identification as well as control parameters. The global uniform stability of the overall system is shown by constructing a Lyapunov function. In this note we treat only the control of a first-order plant in detail, to get across the principal concepts involved. The extension of the results to general nthorder plants can be found in [1] and [2].