Barrier Lyapunov Functions and Constrained Model Reference Adaptive Control

In classical model reference adaptive control, the closed-loop system’s ability to track a given reference signal can be tuned by choosing the adaptive rates and parameterizing the solution of an algebraic Lyapunov equation that appears in the adaptive law. The projection operator can be employed to impose user-defined constraints on the adaptive gains. However, using the projection operator and quadratic Lyapunov functions to certify uniform ultimate boundedness of the trajectory tracking error, the bounds on the trajectory tracking error can only be estimated, but not explicitly imposed
a priori
. In this letter, we provide an adaptive control law for the same class of nonlinear dynamical systems as classical model reference adaptive control. A barrier Lyapunov function guarantees that user-defined constraints on both the trajectory tracking error and the adaptive gains are verified.