This paper deals with some new outcomes on the multi-dimensional control optimisation problem with data uncertainty (UMCOP). By employing the exact $l_1$ penalty function method, we formulate an equivalent unconstrained control optimisation problem and obtain the robust saddle-point criteria for (UMCOP). After that, we show the equivalences between the robust saddle-point of the considered control problem (UMCOP) and a robust minimiser of its associated penalised unconstrained control optimisation problem (UMCOP)${}_{\rho }$. We also provide some numerical illustrations to verify the developed results in this paper.

中文翻译：

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具有数据不确定性的多维控制优化问题的鲁棒鞍点准则

本文讨论了具有数据不确定性的多维控制优化问题 (UMCOP) 的一些新成果。通过采用准确的${升}_1$惩罚函数方法，我们制定了一个等效的无约束控制优化问题，并获得（UMCOP）的鲁棒鞍点准则。之后，我们展示了所考虑的控制问题（UMCOP）的鲁棒鞍点与其相关的惩罚无约束控制优化问题（UMCOP）的鲁棒最小化器之间的等价性${}_{\rho }$. 我们还提供了一些数值插图来验证本文中的开发结果。