This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of computational effort, we rely on this specific data-driven technique, using both solution and desired state measurements to extract the underlying system dynamics. Thus, after the Dynamic Mode Decomposition operators construction, we reconstruct and perform future predictions for all the variables of interest at a lower computational cost with respect to the standard space-time discretized models. We test the methodology in terms of relative reconstruction and prediction errors on a boundary control for a Graetz flow and on a distributed control with Stokes constraints.
翻译:事实上,由于这些问题的数字解决方案需要大量计算努力,因此我们依靠这种特定的数据驱动技术,利用解决方案和理想的状态测量来提取潜在的系统动态。 因此,在动态模式分解运营商建造后,我们重建和未来预测所有感兴趣的变数,以较低的计算成本对标准空间分解模型进行计算。 我们测试了Graetz流动边界控制相对重建和预测错误的方法,以及斯托克斯限制的分散控制方法。