Fast Analytical Solver for Fuel-Optimal Speed Trajectory of Connected and/or Automated Vehicles

A longitudinal fuel-optimal speed trajectory has been found to be a control sequence of four possible modes: maximum acceleration, constant speed cruising, coasting, and maximum braking. However, a numerical optimization solver is required, which has been shown to have a tradeoff between computing efficiency and optimality. This article presents a fast analytical solver that computes the longitudinal fuel-optimal speed trajectory for connected and automated vehicles (CAVs). We formulate a longitudinal fuel-optimal control problem and transform it into a boundary value problem (BVP) through Pontryagin’s minimum principle. By analyzing the costate dynamics of the BVP, we investigate the underlying mechanism required to build the control sequences that consist of multiple modes for a given boundary condition (BC). This approach allows us to identify feasible control sequences and establish feasible criteria for BC for each sequence. Unlike BVP numerical solvers that require a good initial guess, initial costates can be analytically obtained by linking each mode that has an explicit solution after the control sequence is specified by BC. Finally, we show that CAVs equipped with the proposed solver lead to significant fuel savings for single and multiple-vehicle scenarios with different CAV penetration rates.