Adaptive Fuzzy Tracking Control Design for a Class of Uncertain Nonstrict-Feedback Fractional-Order Nonlinear SISO Systems

In this article, a class of uncertain nonstrict-feedback fractional-order nonlinear single-input-single-output (SISO) systems is investigated. Fuzzy-logic systems (FLSs) are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems. For the states measurable case, an adaptive fuzzy state-feedback control scheme is developed under the framework of the backstepping technique. For the states unmeasurable case, an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control (DSC) technique. Under the drive of the reference signals, the semiglobally uniformly ultimate boundedness for all signals and the tracking errors converging to a small neighborhood of the origin are proved based on the Lyapunov function theory by choosing appropriate design parameters. Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.