Historical Data-Driven Composite Learning Adaptive Fuzzy Control of Fractional-Order Nonlinear Systems

Different from traditional adaptive fuzzy control, this paper introduces a composite learning adaptive backstepping fuzzy control method using historical data which mainly focuses on improving the approximation accuracy of fuzzy logic systems for functional uncertainties of fractional-order nonlinear systems. A command filter is employed to settle the explosion of complexity issue that resulted from differentiating virtual controllers repeatedly in each backstepping step, and a compensation signal is defined to reduce the impact of filtered errors on control performance. In addition, a modified prediction error is defined to construct a composite parameter adaptation law, where the compensated error dynamic system equation is integrated in a moving time interval such that all historical data are integrated into a regressor vector to calculate the prediction error. The method introduced can not only ensure the boundedness of all signals in the closed-loop system based on the fractional Lyapunov stability criterion, but also realize the precise approximation to functional uncertainties. Finally, two numerical simulation examples are presented to demonstrate the superior effect of the proposed method.

Automated summary

This paper proposes a composite learning adaptive backstepping fuzzy control method using historical data to improve the approximation accuracy of fuzzy logic systems for functional uncertainties of fractional-order nonlinear systems. The method employs a command filter to resolve the complexity issue caused by differentiating virtual controllers repeatedly, and defines a compensation signal to reduce the impact of filtered errors on control performance. A modified prediction error is also introduced to construct a composite parameter adaptation law by integrating the compensated error dynamic system equation. The method ensures the boundedness of all signals in the closed-loop system and achieves precise approximation to functional uncertainties. Numerical simulation examples demonstrate the superiority of the proposed method.