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Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems

机译：特征向量近似二分法基础方法求解超灵敏最优控制问题

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摘要

The dichotomic basis method is further developed for solving completely hyper-sensitive Hamiltonian boundary value problems arising in optimal control. For this class of problems, the solution can be accurately approximated by concatenating aninitial boundary-layer segment, an equilibrium segment, and a terminal boundary-layer segment. Constructing the solution in this composite manner alleviates the sensitivity. The method uses a dichotomic basis to decompose the Hamiltonian vector field into its stable and unstable components, thus allowing the missing initial conditions needed to specify the initial and terminal boundary-layer segments to be determined from partial equilibrium conditions. The dichotomic basis reveals the phase-space manifold structure in the neighbourhood of the optimal solution. The challenge is to determine a sufficiently accurate approximation to a dichotomic basis. In this paper we use an approximate dichotomic basis derived from local eigenvectors. An iterative scheme is proposed to handle the approximate nature of the basis. The method is illustrated on an example problem and its general applicability is assessed.
机译：为了解决在最优控制中出现的完全超灵敏汉密尔顿边值问题，进一步开发了二分法基础方法。对于此类问题，可以通过串联初始边界层段，平衡段和末端边界层段来精确地近似求解。以这种复合方式构造解决方案可降低灵敏度。该方法使用二分法将哈密顿向量场分解为其稳定和不稳定的分量，从而允许从局部平衡条件确定指定初始边界层段和终止边界层段所需的缺失初始条件。二分法基础揭示了最佳解附近的相空间流形结构。挑战在于确定足够精确的二分法近似值。在本文中，我们使用源自局部特征向量的近似二分法基础。提出了一种迭代方案来处理基础的近似性质。举例说明了该方法，并评估了其一般适用性。

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