SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2288-2311, January 2020.
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for a control that steers the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. Numerical examples with optimal Neumann control of the wave equation are presented.

中文翻译：

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具有不确定初始数据和概率终端约束的振动弦的最优Neumann边界控制

SIAM控制与优化杂志，第58卷，第4期，第2288-2311页，2020年1月。
在最佳控制问题中，通常需要实际中不知道的初始数据。为了考虑这种不确定性，我们考虑了具有不确定初始状态的系统的最优控制问题。给出了有限的终止时间。由于初始状态的不确定性，不可能规定确切的终端状态。相反，我们正在寻找一种控件，该控件以足够高的概率将系统引导到所需终端状态的给定邻域中。根据终端能量的不等式描述该邻域。所考虑的最优控制问题中的概率约束导致了针对初始状态的不可避免不确定性具有鲁棒性的最优控制。