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.

Perspectives

This study shows that it is not sufficient to remain always in an L^2 framework for the application of optimal controls for hyperbolic systems. Even for the optimal control of the linear wave equation the total variation of the given initial and the desired terminal state is important for the implementability of the optimal control to desensitize the optimal control to the effects of time delay.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

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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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