In this paper, considering the applications of interval analysis in various fields (such as artificial intelligence, neural computation, genetic algorithms, information theory or fuzzy logic), a new class of interval-valued variational control problems governed by multiple integral functionals, first-order PDE and inequality constraints is studied. More precisely, efficiency conditions for the considered uncertain variational control problem are formulated and proved. The sufficiency of Karush–Kuhn–Tucker conditions is established under some invexity and \((\rho, b)\)-quasiinvexity assumptions of the involved functionals. In addition, the paper is completed with illustrative applications (describing the controlled behavior of an artificial neural system) and the corresponding algorithm.

在本文中，考虑到区间分析在各个领域（例如人工智能，神经计算，遗传算法，信息论或模糊逻辑）的应用，一类由多重积分函数控制的新型区间值变分控制问题首先是：研究了PDE阶数和不等式约束。更准确地说，制定并证明了所考虑的不确定变控制问题的效率条件。Karush–Kuhn–Tucker条件的充分性是在某些凸度和所涉及功能的\（（\ rho，b）\）-准凸度假设下建立的。此外，本文还完成了说明性应用程序（描述了人工神经系统的受控行为）和相应的算法。