论文标题
使用PASA解决数学生物学中的单数控制问题
Solving Singular Control Problems in Mathematical Biology, Using PASA
论文作者
论文摘要
在本文中，我们将演示如何使用称为多面体主动集合算法（PASA）的非线性多面体约束优化求解器来解决一般的单数控制问题。我们提出了离散一般最佳控制问题的方法，该方法涉及使用拉格朗日的梯度计算成本功能的梯度，以便可以应用PASA。当数值解决方案包含类似于“ chat不休”的伪像，在这种现象中，控制控制沿着奇异区域疯狂地振动时，我们建议一种通过在成本函数中添加一个术语来衡量奇异控制问题的方法，该术语衡量了衡量控制的总体变化的标量的量表，并在其中显示出了一个问题，即在其中显示了一个问题。数学生物学。
In this paper, we will demonstrate how to use a nonlinear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general singular control problem. We present methods of discretizing a general optimal control problem that involves the use of the gradient of the Lagrangian for computing the gradient of the cost functional so that PASA can be applied. When a numerical solution contains artifacts that resemble "chattering'', a phenomenon where the control oscillates wildly along the singular region, we recommend a method of regularizing the singular control problem by adding a term to the cost functional that measures a scalar multiple of the total variation of the control, where the scalar is viewed as a tuning parameter. We then demonstrate PASA's performance on three singular control problems that give rise to different applications of mathematical biology. We also provide some exposition on the heuristics that we use in determining an appropriate size for the tuning parameter.
