The Lyapunov second method is used to derive a control law that can be used
to control the spacing between vehicles in a platoon, A third-order system
is adopted to model the vehicle and powertrain dynamics. In addition, the
concept of "expected spacing error" is introduced and used to form a Lyapun
ov function. Then a control law that always decreases the Lyapunov function
is selected. A platoon of four vehicles and various scenarios are used to
demonstrate the performance of the proposed control law.