01633nas a2200121   4500008004100000245014500041210006900186520106800255100002201323700001701345700002101362856012801383       2020                        eng d00aPOD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations0 aPODGalerkin Model Order Reduction for Parametrized Nonlinear Tim3 a<p>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.</p>1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/pod-galerkin-model-order-reduction-parametrized-nonlinear-time-dependent-optimal-flow