Nonlinear Fractional Uncertain Systems With Quantized Input: Adaptive Backstepping-Based Controller Design

This work explores the development of backstepping-based adaptive control for a class of nonlinear fractional-order systems that encounter systematic uncertainties, time-varying external disturbances, and quantized control input. A novel analog chain rule computation method is proposed to overcome the difficulty in handling the fractional derivatives of composite functions (i.e., virtual control signals) encountered in intermediate recursive steps of the backstepping procedure. A quantified adaptive controller is strictly crafted to guarantee the stability of the system, with all closed-loop signals staying within bounds and the system output tracking error converging to an adjustable residual set asymptotically, leveraging the direct fractional Lyapunov method and such an approach. The simulated studies confirm the efficacy of the investigated control strategy.