Asymptotic approximation for loops with self-organizing optimal regulators of binomial type (Q1594318)

In a previous paper [Dokl. Akad. Nauk 364, No. 6, 752-755 (1999)], the author stated some results related to two-loop self-organizing optimal regulators with extrapolation (SORE), and here, he once more considers a SORE loop with a similar general structure. It is shown that in the special case of binomial coefficients, the mathematical model of the closed loop is represented by a serially connected chain of \(n\) inertial (aperiodic first-order) links with time constants equal to unity. This property generates many interesting features (level of noises, automatic compensation in short time interval, smoothing of external perturbations,\dots,) which opens interesting prospects of applications for the SORE.