Decentralized Merging Control in Traffic Networks with Noisy Vehicle Dynamics: a Joint Optimal Control and Barrier Function Approach

Abstract

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from two roads at a merging point where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to a speed-dependent safety constraint and to speed and acceleration constraints. Implementing the decentralized solution to this problem obtained in prior work is limited by the computational cost when constraints become active on an optimal CAV trajectory and by the presence of noise in the vehicle dynamics. In this paper, we combine the unconstrained optimal control solution (treated as a reference trajectory for each CAV) with control barrier functions (CBFs) that guarantee the satisfaction of all constraints and provide robustness to noise. To accomplish this, we design a joint optimal control and barrier function (OCBF) controller where a CBF-based controller tracks the optimal control trajectory for each CAV in the presence of noise. In addition, when considering more complex objective functions for which analytical optimal control solutions are unavailable, we adapt the CBF method to such objectives. Simulation examples are included to compare the performance of the OCBF controller to optimal solutions (when available) and to a baseline provided by human-driven vehicles with results showing significant improvements in both metrics.