Feedback control of parametrized PDEs via model order reduction and dynamic programming principle (Q1987746)

The authors propose an offline-online splitting approach to approximate the feedback control functions for the infinite horizon optimal control problem with parametrized partial differential equations. In the paper, the control problems are projected onto low-dimensional spaces using the ideas of \textit{A. Schmidt} et al. [ESAIM, Control Optim. Calc. Var. 24, No. 1, 129--151 (2018; Zbl 1170.35066)] and a grid is constructed by a novel estimating statistical information strategy. To reduce the number of basis functions, the authors propose a parameter partitioning technique. The semi-Lagrangian scheme and the dynamic programming principle are used to obtain the parametrized value function for the Hamilton-Jacobi-Bellman equation and to approximate the feedback control. Three examples of optimal feedback control problems are considered to demonstrate the quality of the proposed approach.