Adaptive fuzzy finite-time backstepping control of fractional-order nonlinear systems with actuator faults via command-filtering and sliding mode technique

Abstract

In the paper, a class of unknown fractional-order nonlinear systems suffering from actuator faults are investigated. Meanwhile, an adaptive finite-time sliding mode control (SMC) approach based on approximation principle of fuzzy logic system (FLS) and backstepping layout is proposed. It is well known that the standard backstepping control has inherent computational complexity. Therefore, a type of fractional-order command filter (CF) is introduced to overcome such a shortcoming, that is, by means of fractional-order CF, the virtual input signal and its fractional derivative can be estimated properly as anticipated. Fractional-order sliding mode surfaces are constructed to diminish the filtering errors such that more better performance is guaranteed. Besides, compared to the conventional backstepping control, the CF-based fuzzy backstepping SMC approach presented in the paper not only shows the superior robustness, but also facilitates to accomplish the desired tracking control objective in finite time. The finite-time stability analysis is established on the basis of fractional-order Lyapunov method. Finally, the effectiveness of the proposed methodology is identified by numerical simulations.