Velocity profile optimization of on road vehicles: Pontryagin's Maximum Principle based approach ☆

Driving profile of on road vehicles has shown to have significant effect on fuel economy. This paper discusses the development of Pontryagin's Maximum Principle (PMP) based solution to determine the energy optimal velocity profile by incorporating the gear shifting, speed limit and road grade constraints simultaneously. In the proposed approach the real world road grade profile and speed limits are approximated by a set of piece-wise constant functions and the corresponding first order necessary conditions are derived. By solving a number of differential equations an analytical solution is generated. Therefore, the computation time of the solution is extremely fast. To verify the global optimality of the solution, the results are compared with dynamic programming (DP) solution that solves the complex and non-linear representative model of the actual test vehicle. The comparison results prove that the generated optimal speed trajectories are very close to global optimal solution.