Sholokhov O. Robust Ellipsoidal Estimation of the States of Linear Controlled Systems with the Limited Disturbance and Interference

Sholokhov O. V. Robust Ellipsoidal Estimation of the States of Linear Controlled Systems with the Limited Disturbance and Interference.  Manuscript. Thesis for a scientific degree of Candidate of Physico-Mathematical Sciences in specialty 01.05.04  System Analysis and Theory of Optimal Solutions.  National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, 2019. In the dissertation, a method for robust ellipsoidal state estimation of linear controlled systems with limited perturbation and interference under conditions of non-statistically specified uncertainty, robust to violations of a priori assumptions regarding the external perturbation and measurement error of the state variable of a system perturbed by one channel and observed by one variable, is developed. The method consists of successive stages, at each of which the statements of the estimation method are introduced and proved. At the end, we give a solution to the problem of estimating the position of a stationary object and the task of estimating the angular orientation of an artificial Earth satellite. Based on the developed evaluation method, methods for assessing the state of technical products in the process of setting them up and increasing their technical and operational characteristics were created and introduced into production. Keywords: linear controlled observable system; phase space of states; external disturbance; set of attainability; Minkowski sum of sets; ellipsoidal approximation; contraction operator; measurement interference; hyperlayer; intersection of sets; robustness; violation of a priori assumptions; multidimensional volume of an ellipsoid; trace of matrix of an ellipsoid.