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 providenumerical tests illustrating this approach.
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Alla, A., Falcone, M. & Kalise, D. A HJB-POD feedback synthesis approach for the wave equation. Bull Braz Math Soc, New Series 47, 51–64 (2016). https://doi.org/10.1007/s00574-016-0121-6
- optimal control
- feedback control
- dynamic programming
- Hamilton-Jacobi-Bellman equation
- Proper Orthogonal Decomposition
- wave equation
Mathematical subject classification
- Primary: 49J20, 49N35, 78M34
- Secondary: 49L20, 93B52