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Analytic Solutions of L∞ Optimal Control Problems for the Wave Equation

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  • M. Gugat

    (Technische Universität Darmstadt)

Abstract

There are very few results about analytic solutions of problems of optimal control with minimal L ∞ norm. In this paper, we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. We start in the zero position and consider a problem of exact control, that is, we want to reach a given terminal state in a given finite time. Our aim is to find a control with minimal L ∞ norm that steers the system to the target. We give the analytic solution for certain classes of target points, for example, target points that are given by constant functions. For such targets with zero velocity, the analytic solution has been given by Bennighof and Boucher in Ref. 1.

Suggested Citation

  • M. Gugat, 2002. "Analytic Solutions of L∞ Optimal Control Problems for the Wave Equation," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 397-421, August.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:2:d:10.1023_a:1016091803139
    DOI: 10.1023/A:1016091803139
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    Cited by:

    1. Martin Gugat & Volker Grimm, 2011. "Optimal boundary control of the wave equation with pointwise control constraints," Computational Optimization and Applications, Springer, vol. 49(1), pages 123-147, May.
    2. Gerdts, Matthias & Greif, Günter & Pesch, Hans Josef, 2008. "Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1020-1032.

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