Abstract

We study an optimal control problem described by a system of linear ordinary differential equations with boundary conditions containing point and integral values of the state variable. The controls occurring in the differential equations and the values of the right-hand sides of the nonlocal boundary conditions are determined in this problem. Necessary conditions for the existence and uniqueness of a solution of the boundary value problem and for the convexity of the objective functional, as well as necessary conditions for the optimality of the parameters to be optimized in the control problem, are studied. The formulas obtained for the gradient of the objective functional of the problem are used in the numerical solution of an illustrative problem. The results of numerical experiments are provided.

中文翻译：

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受控动力系统中非局部边界条件右手边的优化

摘要

我们研究由线性常微分方程系统描述的最优控制问题，该系统具有包含状态变量的点和积分值的边界条件。在该问题中确定了在微分方程中出现的控制和非局部边界条件的右侧的值。研究了边值问题的解的存在和唯一性以及目标函数的凸性的必要条件，以及控制问题中要优化的参数的最优性的必要条件。为问题的目标函数的梯度而获得的公式用于说明性问题的数值解中。提供了数值实验的结果。