Conditions for Improving the Computational Efficiency of Decentralized Optimal Merging Controllers for Connected and Automated Vehicles

A solution to a decentralized optimal merging problem for Connected and Automated Vehicles (CAVs) was provided in earlier work. When no safety and state/control constraints are active, optimal trajectories are simple to implement on line, whereas trajectories with constrained arcs become computationally expensive to derive. In this paper, we prove simple-to-check conditions on whether the speed-dependent safety constraint for each CAV remains inactive, which are stronger than former results. We also derive conditions on whether speed constraints remain inactive. This significantly simplifies the online determination of an explicit decentralized solution for each CAV. These simple-to-check conditions also allow us to easily create a Feasiblity Enforcement Zone (FEZ) such that both the safety and speed constraints are not active in the control zone. Simulation examples are included to demonstrate that a large fraction of CAVs satisfy these conditions under common traffic rates, hence improving computational efficiency.