  This paper studies an optimal control problem for a string of vehicles with
safety requirements and finite-time specifications on the approach time to a
target region. Our problem formulation is motivated by scenarios involving
autonomous vehicles circulating on arterial roads with intelligent management
at traffic intersections. We propose a provably correct distributed control
algorithm that ensures that the vehicles satisfy the finite-time specifications
under speed limits, acceleration saturation, and safety requirements. The
safety specifications are such that collisions can be avoided even in cases of
communication failure. We also discuss how the proposed distributed algorithm
can be integrated with an intelligent intersection manager to provide
information about the feasible approach times of the vehicle string and a
guaranteed bound of its time of occupancy of the intersection. Our simulation
study illustrates the algorithm and its properties regarding approach time,
occupancy time, and fuel and time cost.
