Adaptive backstepping control for fractional order systems with input saturation

A fractional order adaptive backstepping control scheme is presented for an incommensurate fractional order systems in the presence of input saturation. In order to compensate the saturation, the necessary signals are generated by constructing a fractional order auxiliary system. Besides the nonlinear functions and unknown parameters of systems, the uncertainties, especially the unknown control input coefficient, are emphasized here. The adoption of fractional order parameters update law and nonlinear feedback has added more degree of freedom to controllers, which leads to a larger range of application. The frequency distributed model is introduced so that the indirect Lyapunov method is available in the procedure of controller design. All the differential signals, used for the control and estimation, are obtained through fractional order tracking differentiator. Compared with previous methods, the backstepping method is first adopted to solve the saturation problem of incommensurate order systems with nonlinearities and uncertainties, which achieves stabilization and tracking. To highlight the effectiveness of the proposed controller, simulation examples are demonstrated at last. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.