Lp-optimal boundary control for the wave equation,

Gugat M, Leugering G, Sklyar G (2005)

Publication Type: Journal article, Original article

Publication year: 2005


Publisher: Society for Industrial and Applied Mathematics

Book Volume: 44

Pages Range: 49-74

Journal Issue: 1

DOI: 10.1137/S0363012903419212


We study problems of boundary controllability with minimal L -norm (p ∈ [2, ∞]) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions. The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the L-norm of the controls. We give necessary and sufficient conditions for the solvability of this problem. We show as follows how this infinite-dimensional optimization problem can be transformed into a problem which is much simpler: The feasible set of the transformed problem is described by a finite number of simple pointwise equality constraints for the control function in the Dirichlet case while, in the Neumann case, an additional integral equality constraint appears. We provide explicit complete solutions of the problems for all p ∈[2, ∞] in the Dirichlet case and solutions for some typical examples in the Neumann case. © 2005 Society for Industrial and Applied Mathematics.

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Gugat, M., Leugering, G., & Sklyar, G. (2005). Lp-optimal boundary control for the wave equation,. SIAM Journal on Control and Optimization, 44(1), 49-74. https://doi.org/10.1137/S0363012903419212


Gugat, Martin, Günter Leugering, and Gregori Sklyar. "Lp-optimal boundary control for the wave equation,." SIAM Journal on Control and Optimization 44.1 (2005): 49-74.

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