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.

中文翻译：

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汽车理论模型的能耗最小化

本文是对具有不可微但Lipschitz成本函数的最优控制问题的研究。它的灵感来自于将已知轮廓的汽车或机器人沿道路的能耗降至最低。通过纵向动力学的简单模型和运行成本来说明该问题，该运行成本包括绝对值函数和考虑能量转换过程效率的函数。证明了从解决方案集中排除颤振现象的规律性结果。它对控制仿射系统类别有效，其中包括所考虑的问题。详细分析了三个案例研究。最佳轨迹显示为爆炸，灭弧，奇异和向后圆弧。