12. Suboptimal Feedback Control of Flow Separation by POD Model Reduction

Optimal Boundary Control Problems Related to High-Lift Configurations

“…A widely used method is POD, [2,15,18,19]. In the case of the high-lift configuration, the application of standard POD does not align to the target of robust dynamical least-order models for the real flow.…”

“…We mention e.g. [2,18,19,35]. A reduced-order model (ROM) is considered in Section 3 due to [20] and [22].…”

A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation

“…The other reason is caused by the curse-ofdimensionality, the inherent defect of the DP approach ( [22]). Thanks to many model reduction techniques ( [1,3,13,20,19]), this problem can be partially circumvented. It makes some effective algorithms for low dimensional problems, thus initially confined to only "toy" problems, can be generalized to deal with much more complicated practical optimal control problems.…”

“…And these methods are tailored to solving the HJBs for both stochastic and deterministic continuous time nonlinear optimal control problems on finite and infinite horizons. The paper [20] considers a distributed volume control problem in infinite time region and obtains the optimal control by the convex combination of the control values at each point of the polyhedron, which can be interpreted as a special interpolation. The idea of using the interpolation to find the optimal control is also mentioned in [13] but it is kept mostly to one-dimensional linear interpolation for one-dimensional problem.…”