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

Maamria, D.; Gillet, K.; Colin, G.; Chamaillard, Y.; Nouillant, C. · 2016 · OpenAlex-citations

DOI: 10.1109/cca.2016.7587980

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Summary

This paper addresses the challenge of solving the Eco-driving Optimal Control Problem (OCP) for conventional vehicles equipped with internal combustion engines. The primary research question is determining which methodology is more appropriate for calculating optimal speed profiles that minimize fuel consumption while adhering to constraints such as fixed travel distance, duration, and speed limits. The study compares two simplified Dynamic Programming (DP) approaches: a "time method" that solves the OCP directly in the time domain, and a "space method" that transforms the problem into a position-based OCP. Both methods utilize the Pontryagin Minimum Principle (PMP) to reduce computational complexity by introducing tunable parameters to satisfy terminal constraints. The authors model a conventional diesel vehicle using longitudinal motion equations, accounting for vehicle mass, rotating inertia, and resistance forces (rolling, aerodynamic, and grade). The OCP formulation minimizes fuel consumption over a fixed horizon, with controls defined by engine torque and gear-box ratio. To solve the problem, the time method fixes the final time and iteratively adjusts a tunable parameter to meet the distance constraint, while the space method fixes the final position and adjusts a parameter to meet the time constraint. Simulations were conducted on a 1930 kg vehicle using two driving cycles: a short cycle (360s, 6.9 km) for method comparison and a more realistic Worldwide Harmonized Light Vehicles Test Cycle (WLTC) extract (588s, 7.6 km) for sensitivity analysis. Results from the short driving cycle indicate that both methods produce comparable speed trajectories and fuel consumption levels. Specifically, the time method achieved slightly lower fuel consumption (216.4 g vs. 217.8 g) but required longer computation time (1200 s vs. 1150 s) compared to the space method. The time method demonstrated higher accuracy at low vehicle speeds, whereas the space method was more accurate at high speeds. In the sensitivity analysis of the space method on the WLTC cycle, the authors evaluated various mesh resolutions for speed and torque. They found that coarser meshes significantly reduced computation time with minimal impact on optimality; for instance, increasing the speed step from 0.01 m/s to 0.05 m/s reduced computation time from 12,000 s to 1,500 s while maintaining nearly identical fuel consumption. The study concludes that the space method is generally more appropriate for solving the eco-driving OCP for conventional vehicles. Although the time method offers marginally better fuel efficiency, the space method provides a superior trade-off between solution optimality and computational efficiency, particularly when using coarser meshes. This makes the space-based DP approach more viable for real-time implementation in driver support systems, where rapid calculation of optimal trajectories is essential. The findings suggest that transforming the time-based OCP into a position-based one effectively mitigates the "curse of dimensionality" associated with DP, enabling practical application in automotive energy management systems.

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• eco driving