Singular Fuel-optimal Control of the Velocity and Power-split of Hybrid Electric Vehicles via Pontryagin's Minimum Principle

This paper studies the eco-driving problem of finding the fuel-optimal velocity and power-split control for parallel hybrid electric vehicles that must drive over a finite distance in limited time. Specifically, we combine Pontryagin's minimum principle and singular control theory to derive the minimum-fuel control policy for the engine and the electric motor, and leverage it to rewrite the original optimal control problem into a Hamiltonian boundary value problem that can be efficiently solved with standard numerical methods. We showcase our findings with numerical simulations, revealing the fuel-optimal strategies favoring a faster, electrically-assisted, initial acceleration so that the required travel distance can be covered at the lowest possible cruising speed