Independent tracking and regulation adaptive control with forgetting factor

This paper considers a discrete-time adaptive control algorithm with a forgetting factor applicable to minimum phase plants. The tracking and regulation objectives are independently specified. The relevance of the eigenvalues of the gain matrix (F_k) used in the updating equation for the adaptive parameters ($\text{}\text{?}\text{gq(k)}$) is shown. It is proved that if the maximum eigenvalue of the inverse of the gain matrix F_k has an upper bound and a non-zero lower bound then the global convergence of the control algorithm is insured. The result of the design is a simple control scheme using a linear constant feedforward controller and a nonlinear feedback controller. The performance of the control structure in tracking and regulation are evaluated by simulations.