ℒ1 Adaptive Controller Design for a Class of Fractional Order Uncertain Systems

ℒ1 adaptive control method is a new and effective technique to perform a robust tracking response with fast adaptation, its applications were generalized for both integer order affine and non-affine nonlinear systems. However, ℒ1 adaptive control scheme has not been yet investigated to control fractional order systems. In this work, an ℒ1 adaptive controller is designed based on a fractional order sliding surface to control a class of fractional order systems with matched uncertainties and external disturbances. The developed controller is able to achieve closed-loop stability with uniform performance bounds for system signals. Such that, increasing the adaptation gain can dramatically enhance the performances for both transient and steady state responses. Finally, the validity and the effectiveness of the controller is tested using a numerical simulation.