Consumption minimization for an academic model of a vehicle. (20th May 2020)

• Record Type: Journal Article
• Authors: Oukacha, Ouazna; Boizot, Nicolas
• Is Part Of: Optimal control applications and methods. Volume 41:Number 4(2020)
• Page Start: 1288
• Page End: 1320
• Publication Date: 2020-05-20
• Subjects: energy consumption minimization -- nondifferentiable cost function -- singular arcs -- regularity; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2604
• Languages: English
• ISSNs: 0143-2087

Abstract

Abstract: 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.