engleski

Control of parameter dependent systems

In this chapter we provide an overview of recent progress on the problem of controlla- bility of parameter dependent systems. We explore different control notions successfullydeveloped through the last decade. The aim of the control function is to steer the systemto a state satisfying some properties prescribed either at some time instantT>0 or dur-ing a given time interval. These properties may be separated with respect to parametervalues and can refer just to a single system itself (e.g. greedy control), or may considersolutions corresponding to the whole parameter range (e.g. ensemble control, averagedcontrol). In the latter case control functions are designed as parameter invariant, implyinga same control is to be applied to the system independently of a particular realization ofthe parameter, while in the first case controls vary along with the parameter.Beside the positive theoretical results, for each notion we provide a precise computationalalgorithm accompanied by a numerical example.Handbook of Numerical Analysis, ISSN 1570- 8659, https://doi.org/10.1016/bs.hna.2021.12.008Copyright © 2022 Elsevier B.V. All rights reserved.1

averaged control ; greedy control ; ensemble control ; parameter dependent systems ; re-duced basis

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