New adaptive laws for model reference adaptive control using a non-quadratic Lyapunov function

Abstract

In the design of model reference adaptive control (MRAC) schemes, adaptive laws have been developed based on Lyapunov stability theory. Over the past few decades, it has been a common practice to use quadratic Lyapunov functions (QLF). In contrast to such development, using a new nonquadratic Lyapunov function (NQLF), this paper presents new adaptive laws for the MRAC. These new laws have the same advantage of assurance of stability of the overall system, as the earlier adaptive laws developed using the QLF. Over and above, they have an additional advantage of improved performance: in fact, the use of NQLF improved the system output error signal converging to zero. Finally, this paper also presents simulation results supporting the arguments.