Abstract

Linear controlled multistep processes are considered with an additive quality functional under a phase constraint and a terminal condition. These processes are of interest for control theory and its applications. An existence theorem for optimum control is proved for the controlled processes under consideration. In analogy with backward constructions in the positional theory of differential games developed to solve positional differential pursuit games, a procedure for geometric splitting is developed for optimizing the considered problems that is characteristic of the theory of dynamic programming.

中文翻译：

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关于线性多步控制过程

摘要

线性控制的多步过程被认为具有在相位约束和最终条件下具有附加质量功能的功能。这些过程对于控制理论及其应用很重要。对于所考虑的受控过程，证明了最优控制的存在性定理。与为解决位置差分追随游戏而开发的差分博弈的位置理论中的后向构造类似，开发了一种用于几何拆分的程序，以优化所考虑的问题，这是动态规划理论的特征。