Optimal control-based feedback stabilization in multi-field flow problems

本课题的目标是推导和研究基于最优控制的多场流问题边界反馈稳定的数值算法。我们将遵循Barbu、Lasiecka、Triggiani、Raymond等人在过去几年的一系列论文中提出的方法。他们已经证明，通过设计一个基于相应的线性二次最优控制问题的稳定控制器，可以稳定由Navier-Stokes方程描述的扰动流。由于现有算法的复杂性，这些线性二次型最优控制问题的数值求解一直是一个数值难题。利用最近的进展，将这些复杂性基本上降低到与正演问题的模拟成比例的成本，我们计划将这种方法应用于流与其他场方程耦合的多场问题。我们提出了三种难度越来越大的情况，我们想要证明基于最优控制的反馈镇定方法的适用性。

The goal in this project is to derive and investigate numerical algorithms for optimal control-based boundary feedback stabilization of multi-field flow problems. We will follow an approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by the Navier-Stokes equation by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem. Until recently, the numerical solution of these linear-quadratic optimal control problem was a numerical challenge due to the complexity of existing algorithms. Employing recent advances in reducing these complexities essentially to a cost proportional to the simulation of the forward problem, we plan to apply this methodology to multi-field problems where the flow is coupled with other field equations. We suggest three scenarios with increasing difficulty for which we want to demonstrate the applicability of the optimal control-based feedback stabilization approach.