论文标题
排名3步骤2的可达到的套装，带有正对照的自由卡诺组
Attainable set for rank 3 step 2 free Carnot group with positive controls
论文作者
论文摘要
我们发现在免费的Carnot Group $ 3 $和Step $ 2 $的免费Carnot Group上的控制系统可实现的设置，并具有正面控制。这种控制系统与自由谎言半群的理论有关。有一些估计的独立随机变量不平等现象的概率；随着机器人控制系统的尼尔疗法近似，以及轮廓恢复，而无需在图像处理中进行尖端。我们借助于时间优势控制问题的庞特蛋白最大原理研究了可实现集的边界。我们研究对应于Bang-Bang，单数和混合对照的极端轨迹。我们获得了最佳控件开关数量的上限。这意味着可达到集合的边界面的参数化。
We find the attainable set for a control system on the free Carnot group of rank $3$ and step $2$ with positive controls. This kind of control systems is connected with the theory of free Lie semigroups; with some estimates for probabilities of inequalities for independent random variables; with the nilpotent approximation of robotic control systems and with contour recovering without cusps in image processing. We investigate the boundary of the attainable set with the help of the Pontryagin maximum principle for the time-optimal control problem. We study extremal trajectories that correspond to bang-bang, singular and mixed controls. We obtain upper bounds for the number of switchings for optimal controls. This implies a parametrization of the boundary faces of the attainable set.
