Volume 13, Issue 1
Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations

L.S. Hou ,  J. Ming and S.D. Yang

Int. J. Numer. Anal. Mod., 13 (2016), pp. 122-144.

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  • 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 L²-norm Dirichlet control and generic, non-smooth minimum L²-norm Dirichlet controls.

  • History

Published online: 2016-01

  • AMS Subject Headings

93B40, 35L05, 65M06

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