Function Space Approach for Gradient Descent in Optimal Control
Function Space Approach for Gradient Descent in Optimal Control
复制标题
最优控制中梯度下降的函数空间方法
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Bassam Bamieh
中科院分区：
文献类型：
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作者：
M. Filo;Bassam Bamieh
基于函数空间中的约束梯度下降法，提出了一种求解开环最优控制问题的迭代数值方法。下降算法使用梯度到流形的切空间上的投影，表示动力学方程的约束。我们的算法的一个关键特点是预处理的二次部分的成本功能与一个相对简单的程序。这种预条件具有简单的几何解释，它给出了直观的推理，快速收敛的局部最优的邻域内的迭代。我们给出了两个典型的例子，包括一个连续搅拌的化学反应器和一个双线性量子系统。该算法的关系，早先提出的Banach空间投影算法的概述。
We develop an iterative numerical method for open-loop optimal control problems based on constrained-gradient descent in function space. The descent algorithm uses a projection of the gradient onto the tangent space of the manifold representing the constraints of the dynamical equation. A key feature of our algorithm is preconditioning of the quadratic portion of the cost functional with a relatively simple procedure. This preconditioning has a simple geometric interpretation, which gives intuitive reasoning for the rapid convergence of the iterations in neighborhoods of local optima. We give two illustrative examples including a continuous stirred-tank chemical reactor, and a bilinear quantum system. The relation of this algorithm to earlier proposed Banach space projection algorithms is outlined.