论文标题
参数化非线性时间依赖性最佳流量控制的POD-Galerkin模型订单减少：应用于浅水方程的应用
POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations
论文作者
论文摘要
在这项工作中，我们建议减少订单方法作为可靠的策略，以有效地解决解决方案跟踪设置中浅水方程控制的参数化最佳控制问题。我们处理的物理参数化模型是非线性和时间依赖性的：这会导致非常耗时的模拟，例如可难以忍受的模拟在海洋环境监测计划中。我们的目的是展示减少的订单建模如何有助于以快速的方式研究不同的配置和现象。构建了最佳系统后，我们依靠Pod-Galerkin降低，以便在低维缩小空间中解决最佳控制问题。提出的理论框架实际上适合一般的非线性时间依赖性最佳控制问题。最终通过数值实验对所提出的方法进行了测试：浅水方程控制的最佳控制问题比标准模型更快地再现了所需的速度和高度轮廓，但仍保持准确。
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.
