论文标题
具有目标误差估计的抛物线PDE的有效模型预测控制
Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation
论文作者
论文摘要
我们展示了如何使用后验目标误差估计来有效地解决模型预测控制（MPC）算法中发生的子问题。在MPC中，仅将计算解决方案的初始部分作为反馈实现，这激发了特别针对这种情况下量身定制的电网细化。为此，我们提出了一个截断的成本功能，作为目标适应性的目标，并在稳定性假设下证明了误差指标在该数量的支持之外呈指数衰减。这导致MPC的时间和空间离散非常有效，我们将通过各种数值示例来说明这一点。
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.
