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A HJB-POD feedback synthesis approach for the wave equation. (English) Zbl 1338.49063

Summary: We propose a computational approach for the solution of an optimal control problem governed by the wave equation. We aim at obtaining approximate feedback laws by means of the application of the dynamic programming principle. Since this methodology is only applicable for low-dimensional dynamical systems, we first introduce a reduced-order model for the wave equation by means of proper orthogonal decomposition. The coupling between the reduced-order model and the related dynamic programming equation allows to obtain the desired approximation of the feedback law. We discuss numerical aspects of the feedback synthesis and provide numerical tests illustrating this approach.

MSC:

49M27 Decomposition methods
49L20 Dynamic programming in optimal control and differential games
49N35 Optimal feedback synthesis
49J20 Existence theories for optimal control problems involving partial differential equations
90C39 Dynamic programming
93B52 Feedback control
35L05 Wave equation
65K10 Numerical optimization and variational techniques
78M34 Model reduction in optics and electromagnetic theory
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