Tracking Differentiator Based Fractional Order Model Reference Adaptive Control: The 1 < α < 2 Case

This article investigates the problem of model reference adaptive control for a class of fractional order linear and nonlinear systems. Based on the fractional order tracking differentiator, the reference model adaptive control scheme is extended to the fractional order systems with the commensurate order 1 <; α <; 2. The stability of closed-loop control system is analyzed using frequency distributed model and Lyapunov stability theorem. Moreover, numerical simulations are performed to demonstrate the effectiveness of the proposed method.