A HJB-POD feedback synthesis approach for the wave equation

作者：Alla Alessandro^*; Falcone Maurizio; Kalise Dante

来源：Bulletin of the Brazilian Mathematical Society, 2016, 47(1): 51-64.

DOI：10.1007/s00574-016-0121-6

• optimal control
• feedback control
• dynamic programming
• Hamilton-Jacobi-Bellman equation
• Proper Orthogonal Decomposition
• wave equation

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.

• 出版日期2016-3