This paper proposes a distributed collision-free control scheme for connected and automated vehicles (CAVs) at a non-signalized intersection. We first divide an intersection area into three sections, i.e., the free zone, the platoon zone, and the control zone. In order to enable the following vehicles to track the trajectory of their leading vehicle in the platoon zone and the control zone, as well as to guarantee the desired distance between any two adjacent vehicles, the distributed platoon controllers are designed. In the control zone, each vehicular platoon is taken as a whole to be coordinated via an intersection coordination unit (ICU). To avoid collision between each pair of the conflicting platoons approaching from different directions, a platoon-based coordination strategy is designed by scheduling the arrival time of each leading vehicle of different platoons. Specially, considering traffic efficiency and fuel economy, the optimal control problem of the leading vehicle is formulated subject to the constraint of allowable minimum arrival time, which is derived from coordination with other approaching platoons. The Pontryagin Minimum Principle (PMP) and phase-plane method are applied to find the optimal control sequences. Numerical simulations show the effectiveness of this scheme.

Previous works have analyzed finite/fixed-time tracking control for nonlinear systems. In these works, achieving the accurate time convergence of errors must be under the premise of known initial values and careful design of control parameters. Then, how to break through the constraints of initial values and design parameters for this issue is an unsolved problem. Motivated by this, we successfully studied prescribed-time tracking control for single-input single-output nonlinear systems with uncertainties. Specifically, we designed a state feedback controller on $[0,T_p)$, based on the backstepping method, to make the tracking error (TE) tend to zero at $T_p$, in which $T_p$ is the arbitrarily selected prescribed-time. Furthermore, on $[T_p,\mathrm{\infty }),$ another controller, similarly to that on $[0,T_p)$, was designed to keep TE within a precision after $T_p$, while TE may not stay at zero. Therefore, on $[T_p,\mathrm{\infty })$, another new controller, based on sliding mode control, was built to ensure that TE stays at zero after $T_p.$