论文标题
解决最佳控制问题的整体惩罚转录的直接方法
A Direct Method for Solving Integral Penalty Transcriptions of Optimal Control Problems
论文作者
论文摘要
我们提出了一种数值方法，用于最小化目标，这些目标受到过度确定不一致的平等约束的大量二次惩罚。这些目标是由二次积分惩罚方法引起的，用于直接转录相等的最佳控制问题。增强拉格朗日方法（ALM）比解决此类问题的二次罚款方法（QPM）具有许多优势。但是，如果离散化的平等约束不一致，则ALM可能不会收敛到最小化目标和罚款术语的无约束偏差的程度。因此，在本文中，我们探讨了适合我们目的的ALM的修改。数值实验表明，修改后的ALM可以比QPM快地最小化某些二次惩罚功能，而未修改的ALM收敛到一个明显不同的问题的最小化器。
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of equality constrained optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM) for solving this class of problems. However, if the equality constraints of the discretization are inconsistent, then ALM might not converge to a point that minimizes the unconstrained bias of the objective and penalty term. Therefore, in this paper we explore a modification of ALM that fits our purpose. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem.
