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    <abstract>This paper deals with feedback control for a linear nonstationary system whose objective is to reach a preassigned set in the state space while satisfying a certain state constraint. The state constraint to be fulfilled cannot be predicted in advance being available only on the basis of observations. It is specified through an adaptive procedure of &quot;guaranteed estimation&quot; and the objective of the basic process is to adapt to this constraint. 

The problems considered in the paper are motivated by some typical applied processes in environmental, technological, economical studies and related topics. 

The techniques used for the solution are based on nonlinear analysis for set-valued maps.</abstract>
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