  Group control of connected and autonomous vehicles on automated highways is
challenging for the advanced driver assistance systems (ADAS) and the automated
driving systems (ADS). This paper investigates the differential game-based
approach to autonomous convoy control with the aim of deployment on automated
highways. Under the non-cooperative differential games, the coupled vehicles
make their decisions independently while their states are interdependent. The
receding horizon Nash equilibrium of the linear-quadratic differential game
provides the convoy a distributed state-feedback control strategy. This
approach suffers a fundamental issue that neither a Nash equilibrium's
existence nor the uniqueness is guaranteed. We convert the individual
dynamics-based differential game to a relative dynamics-based optimal control
problem that carries all the features of the differential game. The existence
of a unique Nash control under the differential game corresponds to a unique
solution to the optimal control problem. The latter is shown, as well as the
asymptotic stability of the closed-loop system. Simulations illustrate the
effectiveness of the presented convey control scheme and how it well suits
automated highway driving scenarios.
