Prescribed Performance-Based Adaptive Fractional Backstepping Control of Integer-Order Nonlinear Systems

In this article, an adaptive fractional backstepping controller is designed for integer-order nonlinear uncertain systems of arbitrary order with prescribed performance subject to unknown time-varying disturbances. The integration of fractional adaptive backstepping control procedure and prescribed performance bound technique, which describes the convergence rate and largest overshoot of the output error, into a unitary framework can result in an enhanced control scheme with high precision. Based on Lyapunov analysis, it is theoretically demonstrated that under the proposed control scheme, all the closed-loop signals remain bounded and the output tracking error with respect to the reference signal, which is strictly confined within the specified performance bound for all time, will asymptotically converge to zero. Simulation studies are presented to show the effectiveness of the proposed fractional adaptive prescribed performance-based control strategy.