CONTROL SYSTEM DEPENDING ON A PARAMETER

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given

An Approach Problem with an Unknown Parameter and Inaccurately Measured Motion of the System

A control system with an unknown constant parameter is considered on a finite time interval. The actual value of the parameter in this control system is unknown to the person controlling the system at the moment when the systems starts moving. Finding an unknown parameter is made by applying a trial control to the control system for a short period of time along with monitoring the corresponding change in the movement of the system. After finding the approximate determination of the unknown parameter we can construct resolving control in the usual way, but we must take into account the additional error associated with the process of approximate determination of the parameter. In this paper, we investigate the influence of the error of measuring phase variable on the accuracy of unknown parameter recovery. © 201

Structural transition in AuAgTe4 under pressure

Gold is inert and forms very few compounds. One of the most interesting of those is calaverite AuTe2, which has incommensurate structure and which becomes superconducting when doped or under pressure. There exist a "sibling" of AuTe2 the mineral sylvanite AuAgTe4, which properties are almost unknown. In sylvanite Au and Ag ions are ordered in stripes, and Te6 octahedra around metals are distorted in such a way that Ag becomes linearly coordinated, what is typical for Ag^{1+}, whereas Au is square coordinated - it is typical for d^8 configurations, i.e. one can assign to Au the valence 3+. Our theoretical study shows that at pressure P_C ~ 5 GPa there should occur in it a structural transition such that above this critical pressure Te6 octahedra around Au and Ag become regular and practically identical. Simultaneously Te-Te dimers, existing at P = 0 GPa, disappear, and material from a bad metal becomes a usual metal with predominantly Te 5p states at the Fermi energy. We expect that, similar to AuTe2, AuAgTe4 should become superconducting above P_C.Comment: 8 pages, 4 figure

Orbitally induced hierarchy of exchange interactions in zigzag antiferromagnetic state of honeycomb silver delafossite Ag3Co2SbO6

We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with N\'eel temperature TN ~ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-flop type) transition below TN in moderate magnetic fields. The GGA+U calculations show the importance of the orbital degrees of freedom, which maintain a hierarchy of exchange interaction in the system. The strongest antiferromagnetic exchange coupling was found in the shortest Co-Co pairs and is due to direct and superexchange interactions between the half-filled xz+yz orbitals pointing directly to each other. The other four out of six nearest neighbor exchanges within the cobalt hexagon are suppressed, since for these bonds active half-filled orbitals turned out to be parallel and do not overlap. The electron spin resonance (ESR) spectra reveal a Gaussian shape line attributed to Co2+ ion in octahedral coordination with average effective g-factor g=2.3+/-0.1 at room temperature and shows strong divergence of ESR parameters below 120 K, which imply an extended region of short-range correlations. Based on the results of magnetic and thermodynamic studies in applied fields, we propose the magnetic phase diagram for the new honeycomb-lattice delafossite

Mathematical Modeling of Non-Stationary Hydraulic Process Occurring in the Gas Centrifuge Cascade During the Separation of Multicomponent Isotope Mixtures

This article presents results of development of the mathematical model of nonstationary separation processes occurring in gas centrifuge cascades for separation of multicomponent isotope mixtures. This model was used for the calculation parameters of gas centrifuge cascade for separation of germanium isotopes. Comparison of obtained values with results of other authors revealed that developed mathematical model is adequate to describe nonstationary separation processes in gas centrifuge cascades for separation of multicomponent isotope mixtures

Control Systems Depending on a Parameter

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.This research was supported by the Russian Science Foundation (project no. 19-11-00105)