Prescribed Performance Adaptive Fixed-Time Attitude Tracking Control of a 3-DOF Helicopter with Small Overshoot

Abstract: In this article, a novel prescribed performance adaptive fixed-time backstepping control strategy is investigated for the attitude tracking of a 3-DOF helicopter. First, a new unified barrier function (UBF) is designed to convert the prescribed performance constrained system into an unconstrained one. Then, a fixed-time (FxT) backstepping control framework is established to achieve the attitude tracking. By virtual of a newly proposed inequality, a non-singular virtual control law is constructed. In addition, a FxT differentiator with a compensation mechanism is employed to overcome the matter of "explosion of complexity". Moreover, a modified adaptive law is developed to approximate the upper bound of the disturbances. To obtain a less conservative and more accurate approximation of the settling time, an improved FxT stability theorem is proposed. Based on this theorem, it is proved that all signals of the system are FxT bounded, and the tracking error converges to a preset domain with small overshoot in a user-defined time. Finally, the feasibility and effectiveness of the presented control strategy are confirmed by numerical simulations.