Abstract

A sweep method is proposed for solving the optimal control problem with unseparated boundary conditions. This model reduces the boundary conditions to the initial condition. Using the properties of the J-symmetry of the corresponding Hamiltonian matrix and Euler–Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric matrix of coefficients. The proposed algorithm allows us to reduce the dimension of the problem of finding the fundamental matrix of the Hamiltonian system. The results are illustrated by the example of a linear-quadratic optimal control problem (stationary case) with the minimal control actions.

中文翻译：

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求解边界条件不分开的连续线性二次最优控制问题的新运行算法

摘要

提出了一种求解边界条件不分开的最优控制问题的扫描方法。该模型将边界条件简化为初始条件。利用相应汉密尔顿矩阵的J对称性和Euler-Lagrange方程的性质，表明用于确定所求解系统的缺失初始数据的线性代数方程具有一个对称的系数矩阵。所提出的算法使我们能够减少寻找哈密顿系统基本矩阵的问题的规模。结果以具有最小控制作用的线性二次最优控制问题（平稳情况）为例。