Optimized Longitudinal Control of Connected Vehicle Platoons Using Differential Game Theory

The longitudinal decision-making control of connected vehicle platoons is critical to ensuring safety and efficiency. This study proposes a differential game-based control strategy for vehicle platoons, incorporating control variables such as vehicle state, accel-eration, and engine delay. A differential game framework is formulated, establishing the objective function and state transition equations based on platooning goals and spacing policies. The longitudinal control problem is then transformed into an optimal control problem, and the Nash equilibrium strategy is derived by solving the Hamilton-Jacobi-Bellman equation. A double-predecessor-following topology is further introduced to refine the objective function. Simulation results in a longitudinal platoon environment demonstrate that, under the TPF topology, the control model reduces spacing error by 48.59%, offering improved stability, accuracy, and safety. This differential game-based strategy effectively meets platooning control objectives and enhances the stability of connected vehicle longitudinal control.