Global Prescribed Performance Control for 2-D Plane Vehicular Platoons With Small Overshoot: A Fixed-Time Composite Sliding Mode Control Approach

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.