Performance enhanced model reference adaptive control through switching non-quadratic Lyapunov functions

Based on the model reference adaptive scheme, a robust adaptive tracking controller for systems with arbitrary relative degree and known high-frequency gain is proposed. To cope with the difficulty raised by swapping lemma for systems with relative degree beyond one, a new variable related to the tracking error is defined. It is also indicated that if the new defined variable converges to zero asymptotically with time, so does the tracking error. In the line of achieving adaptation laws, a non-quadratic Lyapunov function with one degree of freedom called αα is considered, where α=1α=1 corresponds to a quadratic Lyapunov function. Effects of choosing different values for αα on the response of the system is studied analytically. It is shown that using a multi-criterion αα may lead to a faster response compared to that of α=1α=1. For enhancing the tracking performance, a switching scheme is designed in a constructive manner. Using projection technique to prevent parameter drift, it is shown analytically that the proposed scheme is robust against bounded disturbances. It is also indicated that for systems with relative degree one, knowing the high-frequency gain can be relaxed. Two examples are presented to show the effectiveness of the proposed approach: (1) a numerical example as a system with relative degree one, (2) the speed control of DC motor as a system with a relative degree larger than one.