Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations
Year: 2016
Author: L. S. Hou, S.-D. Yang
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 122–144
Abstract
Numerical solutions of optimal Dirichlet boundary control problems for linear and semilinear wave equations are studied. The optimal control problem is reformulated as a system of equations (an optimality system) that consists of an initial value problem for the underlying (linear or semilinear) wave equation and a terminal value problem for the adjoint wave equation. The discretized optimality system is solved by a shooting method. The convergence properties of the numerical shooting method in the context of exact controllability are illustrated through computational experiments. In particular, in the case of the linear wave equation, convergent approximations are obtained for both smooth minimum $L^2$-norm Dirichlet control and generic, non-smooth minimum $L^2$-norm Dirichlet controls.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-430
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 122–144
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Controllability optimal control wave equation shooting method finite difference method.