Prescribed Performance Adaptive Tracking Control With Small Overshoot for a Class of Uncertain Second-Order Nonlinear Systems

Abstract

This brief investigates the problem of prescribed performance adaptive tracking control for a class of second-order nonlinear systems with uncertainties. First, a new performance function is defined to guarantee that the tracking error has small overshoot and converges to a predetermined region for a user-defined time. Then, to effectively diminish the control input energy consumption caused by the introduction of constraints, a novel coordinate transformation function is designed. Next, an improved fixed-time backstepping control framework is established to achieve the tracking control objective. According to the theoretical analysis, all signals of the closed-loop system are bounded, and the tracking error converges to a preset domain with small overshoot for a user-designed time. Finally, numerical simulations confirm the effectiveness of the presented control strategy.