Observer-based Adaptive Fuzzy Control for Nonlinear Fractional-Order Systems via Backstepping and Sliding Mode Techniques

Compared with integral-order calculus, fractional calculus is better at depicting the real process with memory property and history-dependent property. As a result, this work investigates a class of nonlinear strict-feedback fractional-order systems and presents a novel control strategy. To begin, in order to cope with the unknown drift functions and unmeasurable system states, fuzzy logic systems (FLSs)and a robust fractional-order state observer are designed. Second, in order to further reduce the FLS approximation error and state estimation error, a hyperbolic tangent function is implemented. Third, the problem of the differential explosion caused by repeated differentiation when employing the backstepping technique when designing a control scheme is also overcome without the help of a command filter or dynamic surface control. Finally, theoretical analysis and simulation results show that by combining the backstepping procedure with the sliding mode technique, not only is it possible to achieve strong robustness against unknown drift function and unknown external time-varying disturbance, but also that the tracking error can converge to the vicinity of the origin.