Optimal Control of Autonomous Vehicles for Flow Smoothing in mixed-autonomy Traffic

This article studies the optimal control of autonomous vehicles over a given time horizon to smooth traffic. We model the dynamics of a mixed-autonomy platoon as a system of non-linear ODEs, where the acceleration of human-driven vehicles is governed by a car-following model, and the acceleration of autonomous vehicles is to be controlled. We formulate the car-following task as an optimal control problem and propose a computational method to solve it. Our approach uses an adjoint formulation to compute gradients of the optimization problem explicitly, resulting in more accurate and efficient numerical computations. The gradients are then used to solve the problem using gradient-based optimization solvers. We consider an instance of the problem with the objective of improving the fuel efficiency of the vehicles in the platoon. The effectiveness of the proposed approach is demonstrated through numerical experiments. We apply the proposed approach to different scenarios of lead vehicle trajectories and platoon sizes. The results suggest that introducing an AV can produce significant energy savings for the platoon. It also reveals that the solution is agnostic to the platoon size thus the fuel saving is mainly due to optimizing the trajectory of the AV.