Abstract

A quadratic functional with linear constraints in the form of differential equations with identically degenerate matrices multiplying the derivative of the state vector function is considered. The structure of the general solutions of such systems and some of their properties are discussed. On this basis, the conditions for the non-negativity of the objective functional and small deviation of the control from the stationary point for small values of the functional are obtained.

中文翻译：

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退化线性二次控制问题的性质与欧拉-泊松方程之间的关系

摘要

考虑具有线性约束的微分方程形式的二次函数，该矩阵具有同样退化的矩阵乘以状态向量函数的导数。讨论了此类系统的一般解决方案的结构及其某些性质。在此基础上，对于小功能值，获得了目标功能非负的条件和控制与固定点的小偏差。