Lyapunov design of least-squares model-reference adaptive control

摘要

A Lyapunov design of a least-squares model-reference adaptive control (LS-MRAC) algorithm is presented. The plants considered are continuous with relative degree one. A Monopoli multiplier, originally proposed to extend the MRAC algorithm to the case of relative degree two, is introduced. As a result, fast convergence of the tracking error is achieved and, moreover, the Lyapunov analysis shows that a quadratic term depending on the parametric error belongs toL2,which improves the stability properties of the system. This is the key feature that allows a more powerful LS algorithm to be employed in the update law. The resulting LS-MRAC seems to be a missing algorithm in the literature. Simulation results illustrate the improvement in the transient behavior as well as in the parameter convergence attained with the proposed adaptive schemes.