Consumption minimization for an academic model of a vehicle

Ouazna Oukacha (1, 2) , Nicolas Boizot (1, 2)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 CDE - Contrôle et Diagnostic pour l’Environnement

The present article is a study of an optimal control problem having a non‐differentiable, but Lipschitz, cost function. It is inspired by the minimisation of the energy consumption of a car‐like vehicle or robot along a road which profile is known. This problem is stated by means of a simple model of the longitudinal dynamics and a running cost that comprises both an absolute value function and a function that accounts for the efficiency of the energy conversion process. A regularity result that excludes chattering phenomena from the set of solutions is proven. It is valid for the class of control affine systems, which includes the considered problem. Three case studies are detailed and analysed. The optimal trajectories are shown to be made of bang‐bang, inactivated, singular and backward arcs.

Mots clés: singular arcs; Energy consumption minimization; regularity; non-differentiable cost function; Non-differentiable cost; energy consumption minimisation

Domaines: Optimisation et contrôle [math.OC]

Ouazna Oukacha, Nicolas Boizot. Consumption minimization for an academic model of a vehicle. Optimal Control Applications and Methods, 2020. ⟨hal-01384651v2⟩