Model reference adaptive control of unknown control gain and asymmetrical static output constraints

The model reference adaptive control (MRAC) issue is addressed for a class of first-order linear time-invariant system (LTIS) with unknown control gain and asymmetric static output constraints. The output constraints is efficiently handled by incorporating a barrier Lyapunov function (BLF). Completely unknown control gain is handled based on the Nussbaum function. By the aid of Lyapunov synthesis method, the adaptive laws of unknown parameters are given. Using the properties of BLF and Barbalat's Lemma, it is proved that the tracking error converges asymptotically to zero while the output satisfies the constraints. The comparison of the two simulation results is employed to demonstrate the efficacy of the suggested MRAC algorithm.