An Improved MRAC Scheme without Prior Knowledge of High-Frequency Gain

This paper develops an improved direct model reference adaptive control (MRAC) scheme for continuous-time systems with high relative degrees. The proposed adaptive control scheme does not require any prior knowledge of the high-frequency gain, thereby eliminating the design constraints on the sign of high-frequency gain in traditional MRAC design. Specifically, this paper incorporates the estimation of tracking error derivatives into the control signal, and constructs a new MRAC law with a tuning gain. Then, the unknown high-frequency gain and unknown MRAC law parameters in the error equation are decoupled, and parameter update laws without prior knowledge of the high-frequency gain are designed. Unlike existing schemes for addressing the unknown high-frequency gain, this scheme does not rely on any additional design conditions and avoids singularity and persistent control switching issues, while still ensuring closed-loop stability and asymptotic output tracking for continuous-time systems with high relative degrees. Finally, the effectiveness of the proposed scheme is demonstrated through the simulation of the aircraft control system.