Stable fractional-order model reference adaptive control

This paper studies a novel adaptive control strategy for a linear system with unknown parameters via fractional calculus (FC). In order to design a control system with better dynamic performances, a new model reference adaptive control (MRAC) system is designed by constructing a fractional-order integral Lyapunov function for the linear system with unknown parameters, and then the stability of the closed-loop system is proved. A simulation example shows that the closed-loop system has much better dynamic performances such as less regulating time and less overshoot than the traditional method.