Decentralized Optimal Merging Control for Mixed Traffic with Vehicle Inference

This paper addresses the optimal control of vehicles arriving from two curved roads at a merging point where the objective is to jointly minimize the travel time, energy consumption, and passenger discomfort. Unlike prior work where traffic consists entirely of Connected and Automated Vehicles (CAVs), we consider optimal controls for CAVs in mixed traffic including Human-Driven Vehicles (HDVs) behaving according to some car-following model that includes random actions. The control applied to CAVs is based on partial information about the presence and states of HDVs which is inferred from local observations available to the CAVs. The passing order of HDVs at the merging point is determined and assisted by CAVs using a proposed Minimum-Effort Merging Contract (MEMC) that uses Control Barrier Functions (CBFs) to guarantee safety. A coordinator is used to manage both the CAV information and inferred HDV information such that the problem can still be solved in a decentralized way. Our approach first determines an analytically tractable unconstrained optimal solution. We then use the joint Optimal Control and Barrier Function (OCBF) method to obtain a controller which optimally tracks such a solution while also guaranteeing all safety and control constraints, including a safe merging contract between CAVs and HDVs. Simulation examples are included to compare the performance under different CAV penetration rates.