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

M. Gugat
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M. Gugat: Technische Universität Darmstadt

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 2, No 7, 397-421

Abstract: 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.

Keywords: optimal control; wave equation; analytic solutions; distributed parameter systems (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1016091803139

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