Solutions of L-p-norm-minimal control problems for the wave equation

Gugat M, Leugering G (2002)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2002


Publisher: Sociedade Brasileira de Matemática Aplicada e Computacional

Book Volume: 21

Pages Range: 227-244

Journal Issue: 1


For p is not 2, only few results abaout analytic solutions of problems of optimal control of distributed parameter systems with LP-norm have been reported in the literature. In this paper we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. The aim is to steer the system from a position of rest to a constant terminal state in a given finite time. Also more general final configurations are considered.

The objective function that is to be minimized is the maximum of the L-p-norms of the control functions at both boundaries. It is shown that the analytic solution is, in fact, independent of the choice of the p norm that is minimized. So the optimal controls solve a problem of multicriteria optimization, with the L-p-norms as objective functions.

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How to cite


Gugat, M., & Leugering, G. (2002). Solutions of L-p-norm-minimal control problems for the wave equation. Computational and Applied Mathematics, 21(1), 227-244.


Gugat, Martin, and Günter Leugering. "Solutions of L-p-norm-minimal control problems for the wave equation." Computational and Applied Mathematics 21.1 (2002): 227-244.

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