Universal controllers for the optimal tracking of signals in linear discrete systems (Q1594076)

A signal tracking problem with a nonobservable noise for linear discrete systems is considered. The main aim of this paper is the construction of an optimal universal regulator (OUR), which should simultaneously be a solution to a family of optimization problems. Further, it is shown that, under the condition that the state coefficient matrix is stable, an OUR exists. However, an optimal regulator only exists if the parameters of the initial system and the real-valued quadratic form belong to some set of zero measure. The authors show that, with some dimensional conditions, an asymptotic tracking exists under any exterior noise. Finally, the \(T\)-universal regulators (implementable and stabilizing) are studied.