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The fixed-time control is investigated for an uncertain two-dimensional (2-D) planar vehicular platoon system with global prescribed performance. First, a novel fixed-time prescribed performance control (FxTPPC) method is designed to guarantee the tracking errors converge to the prescribed region with small overshoot inside a predefined time. Moreover, the restriction of PPC method that relies on the initial condition of tracking errors is also released, which means global PPC can be achieved. Then, a new control scheme, by virtue of the composite fixed-time sliding mode surface, is constructed for the third-order 2-D plane platooning system, such that the tracking errors, including distance errors and heading errors, approach to a predetermined region in a given time, while avoiding the singularity problem and improving the convergence rate of the system. In addition, fixed-time string stability and reachability of fixed-time prescribed performance are also achieved. Finally, by constructing numerical simulations and experiment studies, the validity of the proposed scheme is demonstrated in the end.
Gao et al. (Mon,) studied this question.