What is it about?
The optimal control of the wave equation is a well-established subject. For feedback controls the destabilizing effects of time delays are well-known. The corresponding effects for optimal controls are studied in this paper. It turns out that arbitrarily small delays in the implementation of the optimal control can have a destabilizing effect.
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Why is it important?
It is important to know the limits of the optimal controls in the L^2 framework. In the paper we show that the effect of time delay in the implementation of optimal controls is limited in terms of the total variation of the problem data.
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This page is a summary of: Time Delay in Optimal Control Loops for Wave
Equations, ESAIM Control Optimisation and Calculus of Variations, June 2016, EDP Sciences, DOI: 10.1051/cocv/2015038.
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