Indirect model reference adaptive control for a class of linear fractional order systems

In this study, fractional order indirect model reference adaptive control method is used to control a class of fractional order systems. Unlike the traditional integer order case, the controller is obtained by Lyapunov method and the closed-loop stability is achieved via indirect Lyapunov method rather than the certainty equivalence principle. Moreover, for the knowledge that the fractional order integral rate is much slower than the integer order case, fractional order updating laws are considered to achieve more steady performances in the system output, parameter estimation, and control input. Finally, a careful simulation example is presented to illustrate the effectiveness of the proposed control method.