Existence of optimal solutions and necessary optimality conditions for a controlled version of Moreau's sweeping process are derived. The control is a measurable ingredient of the dynamics and the constraint set is a polyhedron. The novelty consists in considering time periodic trajectories, adding the requirement that the control has zero average, and considering an integral functional that lacks weak semicontinuity. A model coming from the locomotion of a soft-robotic crawler, that motivated our setting, is analysed in detail. In obtaining necessary conditions, a variant of the method of discrete approximations is used.

中文翻译：

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与速率无关的软履带的最优控制

得出了Moreau清扫过程的受控版本的最优解的存在和必要的最优条件。控件是动力学的可测量成分，约束集是多面体。新奇之处在于考虑了时间周期轨迹，增加了对控制具有零平均值的要求，并考虑了缺乏弱半连续性的积分函数。我们详细分析了一个模型，该模型来自于软机器人爬虫的运动，从而激发了我们的环境。在获得必要条件时，使用了离散近似方法的一种变体。