Information-theoretic lower bounds in a nonparametric problem of adaptive control (Q1594059)

The authors consider a control problem governed by a nonlinear difference equation with a random unobservable perturbation \[ y_n= -g(y_{n-1})+ u_{n-1}+ \xi_n,\quad n= 1,2,\dots\;. \] Here \(u_n\) is a control, \(\xi_n\) is a random unobservable perturbation, \(E(\xi_n)= 0\), \(E(\xi^2_n)= \sigma^2> 0\), \(g\) a real-valued measurable function with certain properties. The objective is to design a control \(u_n\) to ensure the minimum possible output variable \(y_n\).