Convergence Analysis of Cooperative Braking Control for Interconnected Vehicle Systems

Cooperative braking control is a very important operation in vehicle platoon control for developing intelligent transportation systems, which can effectively increase road capacity, decrease safety hazard, and avoid serial rear-end collisions. This paper focuses on cooperative braking control of autonomous vehicles, the objectives of which are to ensure intervehicles keep within the safe spacing range and rapidly, smoothly, and accurately stop at the desired target stopping positions with zero velocity. To achieve these goals, a three-vehicle platoon framework is presented and the corresponding dynamic model is established based on only information about front-end and rear-end sensors of vehicles, so communication is not needed. The explicit solutions on the three-vehicle platoon are derived by rigorous convergent analysis and detailed proof, such that intrinsic characteristic of the interconnected vehicles is revealed. The resulting convergent conditions and convergent rate are obtained under three cases including: 1) considering internal virtual forces; 2) considering external braking forces; and 3) considering both the internal virtual forces and external braking forces simultaneously. Moreover, an example is further provided to verify that the derived convergence conditions are effective and sufficient under the different controller parameter selection. These results can provide a solution for a wide class of interconnected systems and a guide for controller design to select control parameters in real engineering applications. Simulation results demonstrate the validity of the proposed control approaches.