Fuzzy Composite Learning Control of Uncertain Fractional-Order Nonlinear Systems Using Disturbance Observer

Noting that in traditional adaptive fuzzy controller (AFC) design, only the convergence of tracking error rather than fuzzy approximation error can be guaranteed. This paper focuses on tracking control of fractional-order systems subjected to model uncertainties together with external disturbances. Firstly, an AFC that blends the fuzzy logic system and the input constraint is proposed, where a disturbance observer is constructed to estimate the compounded disturbance. To improve the fuzzy approximation performance, a fractional-order serial parallel estimation model that combines with a fuzzy logic system and a disturbance observer is exploited to generate prediction errors, and both tracking errors and prediction errors are utilized simultaneously to construct parameter update laws, so that a composite learning fuzzy controller (CLFC) is implemented. In addition, a compound disturbance observer is proposed based on the system state and the prediction error while the disturbance estimation error is ensured to remain inside a bounded closed set. The proposed CLFC can not only assure the stability of the closed-loop system but also achieve an accurate estimation of function uncertainties and unknown compounded disturbances. Finally, the effectiveness of the proposed control algorithm is demonstrated via simulation results.