Computational optimal control of 1D colloid transport by solute gradients in dead-end micro-channels
Computational optimal control of 1D colloid transport by solute gradients in dead-end micro-channels
复制标题
死端微通道中溶质梯度对一维胶体输运的计算优化控制
DOI：
10.3934/jimo.2018052
复制
发表时间：
2018-04
影响因子：
1.3
通讯作者：
Zhigang Ren
中科院分区：
文献类型：
--
作者：
Tehuan Chen;Chao Xu;Zhigang Ren
扩散电泳是胶体在非均匀溶质浓度条件下的一种常见现象。它产生溶质梯度，迫使胶体朝向或远离较高溶质浓度侧转移。本文研究了在药物输送、生物输送、采油系统等方面有着广泛应用的具有边界溶质浓度可控的闭端微通道中胶体输运的输入顺序控制问题，采用溶质扩散方程和胶体输运模型的耦合系统对该过程进行了建模。然后，最优控制问题，其中的目标是最小化之间的计算一个和目标的胶体密度分布偏差在预先指定的终端时间。为了解决这个偏微分方程（PDE）的最优控制问题，我们首先应用控制参数化的方法来离散边界控制，并将其转化为一个最优参数选择问题。然后，使用变分法，可以导出目标函数关于决策参数的梯度，这取决于耦合系统和共态系统的解。在此基础上，我们提出了一种有效的计算方法和基于梯度的优化算法来数值求解最优控制问题。仿真结果表明，基于该方法的目标函数比定值控制策略的目标函数小近两个数量级，说明了该方法的有效性。
Diffusiophoresis is a common phenomenon that occurs when colloids are placed in the non-uniform solute concentration. It generates solute gradients which force the colloids to transfer toward or away from the higher solute concentration side. In this paper, we consider the input sequence control of the colloid transport in a dead-end micro-channel with a boundary solute concentration being manipulated, which has a wide range of applications such as drug delivery, biology transport, oil recovery system and so on. We model this process by a coupled system, which involves the solute diffusion equation and the colloid transport model. Then an optimal control problem is formulated, in which the goal is to minimize colloid density distribution deviation between the computational one and the target at a pre-specified terminal time. To solve this partial differential equation (PDE) optimal control problem, we first apply the control parameterization method to discretize the boundary control and transfer it into an optimal parameter selection problem. Then, using the variational method, the gradient of the objective function with respect to the decision parameters can be derived, which depends on the solution of the coupled system and the costate system. Based on this, we propose an effective computational method and a gradient-based optimization algorithm to solve the optimal control problem numerically. Finally, we give the simulation results to demonstrate that the objective function based on the proposed method is less nearly two orders of magnitude than that of a constant value control strategy, which well illustrates the effectiveness of the proposed method.
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影响因子：
3.1
作者：
通讯作者：
--
DOI：
--
发表时间：
1982-10
期刊：
--
影响因子：
--
作者：
Y. Lu;T. Williams
通讯作者：
Y. Lu;T. Williams
使用时间尺度技术对 Saint-Venant PDE 模型进行计算最优控制
影响因子：
1.8
作者：
Chen Tehuan;Chao Xu
通讯作者：
Chao Xu
影响因子：
1.3
作者：
Song Wang;X. Lou
通讯作者：
Song Wang;X. Lou
影响因子：
4.3
作者：
O. Rosen;R. Luus
通讯作者：
O. Rosen;R. Luus