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The sensitivity of optimal states to time delay
Author(s) -
Gugat Martin,
Herty Michael
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410370
Subject(s) - computation , optimal control , norm (philosophy) , control theory (sociology) , energy (signal processing) , control (management) , transmission (telecommunications) , computer science , boundary (topology) , mathematics , mathematical optimization , telecommunications , algorithm , mathematical analysis , statistics , artificial intelligence , political science , law
Abstract In the design and computation of optimal controls for systems that evolve in time, usually the effect of delay is ignored. However in the implementation of the computed optimal controls in the control systems often delays occur, for example through transmission via digital communication channels. The question to be addressed is whether such small delays can have large effects on a system that is steered by an optimal control. We show that for a system that is governed by the wave equation with L 2 ‐norm minimal exact Dirichlet boundary control, for arbitrarily small time‐delays there are initial states such that the terminal energy is almost twice as big as the initial energy. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)