Universal controllers for optimal damping of forced oscillations in linear discrete systems
The paper deals with the difference linear system \[ x_{n+1}=Ax_n+Bu_n+Ew_n,\quad y_n=Cx_n, \] where \(x_n\) is the state, \(y_n\) is the output, \(u_n\) is a control, \(w_n\) is the unobserved external action. The aim of the control is to minimize a functional \(F\) which characterizes the level of oscillations in a system with a given real quadratic form. The functional \(F\) depends on the unknowns \(w_n.\) Since their values are not known, the authors state the problem of finding an optimal controller that does not depend on these values. Such a controller is called an optimal universal controller. Three theorems give existence conditions for the universal controller in some classes of controllers. Moreover stochastic external actions are considered.
scientific article; zbMATH DE number 1564297