Alternative to the Well-known Statistical Dynamics of Linear Systems

TL;DR

This paper proposes an alternative statistical dynamics approach for multi-dimensional control systems affected by noise, especially when correlation functions are unavailable, using frequency methods and set systems of signals.

Contribution

It introduces a novel frequency-based method for modeling noisy control systems without relying on correlation functions, utilizing set systems of signals and deterministic functions.

Findings

Effective noise handling in control systems without correlation functions

Application to aircraft dynamic characteristic determination

Demonstrated on automatic landing data

Abstract

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems is a more effective alternative. Background information is presented in the form of individual implementations nonergodic stochastic processes. Such a realization is deterministic functions. We introduce the concept of systems of sets of signals for the components on the semiring. For the system of sets of linearly dependent and linearly independent of the measured signals of a certain frequency properties. Frequency method is designed to deal with the noise on the set of deterministic functions. Example is the determination of the dynamic characteristics of the aircraft in accordance with the data obtained in one automatic landing.