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A HJB-POD feedback synthesis approach for the wave equation

  • Alessandro Alla
  • Maurizio Falcone
  • Dante Kalise
Article

Abstract

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.

Keywords

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 

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Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  • Alessandro Alla
    • 1
  • Maurizio Falcone
    • 2
  • Dante Kalise
    • 3
  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany
  2. 2.Dipartimento di MatematicaSapienza Università di RomaRomeItaly
  3. 3.Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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