Which methodology is more appropriate to solve Eco-driving Optimal Control Problem for conventional vehicles?

Abstract

Abstract-In this paper, two simplified methods based on Dynamic Programming (DP) to solve an Eco-driving problem for a conventional vehicle equipped with an internal combustion engine are studied. The first method is based on the transformation of a time-based Optimal Control Problem (OCP) into a distance-based OCP while the second is based on solving the time-based OCP directly. The Pontryagin Minimum Principle (PMP) is used to decrease the complexity of the OCP formulation. Based on simulations, the two methods are compared in terms of optimality (fuel consumption) and the time needed to run the DP. The impact of the mesh choice on the optimality of the solution is also investigated.

Computation of eco-driving cycles for Hybrid Electric Vehicles: Comparative analysis

“…A comparison between the time-based and the space-based OCP solutions for a conventional vehicle is given in (Maamria et al, 2016b). If the position space is discretized in N points with a fixed step ∆x, the time step ∆t(k), k = 1 : N is variable and is implicitly calculated from the vehicle speed v(k) and the vehicle acceleration a(k) by solving the second order equation…”

Optimal eco-driving for conventional vehicles: Simulation and experiment

“…The chosen approach transforms a time-based OCP into a distance-based OCP as suggested in (F. Mensing, 2013;Monastyrsky and Golownykh, 1993;Bouvier et al, 2015) in order to reduce the computation time (a comparison between the time-based and the space-based OCP solutions is given in (Maamria et al, 2016)). …”

“…The constant tunable parameter β penalizes the final time to obtain almost the same time duration as the initial driving cycle: the study in (F. Mensing, 2013;Maamria et al, 2016) shows that the relation between t f = ∑ N k=1 ∆t(k) and β is monotone. A root-finding method could be used to drive the final time error to zero (Mensing et al, 2011;Sciarretta et al, 2015).…”

Optimal Predictive Eco-Driving Cycles for Conventional, Electric, and Hybrid Electric Cars

“…Urban and ∆x = 20m for the other driving cycles. These values of ∆x were chosen so as to have a time step approximately around 1s [33]. Two cases are studied: electric and conventional.…”

“…The control variables are the engine torque T e and the gear-box ratio R gb . The following DP mesh parameters are chosen based on the results presented in [33]: ∆v = 0.1m/s for the vehicle speed and ∆T e = 2N.m for the engine torque 2 . For scenario I, the results in terms of fuel consumption, fuel saving through eco-driving with respect to the initial driving cycles and computation time of the DP t co are given in Table VII.…”