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

Robotic optical telescopes global network MASTER II. Equipment, structure, algorithms

Presented paper describes the basic principles and features of the implementation of a robotic network of optical telescopes MASTER, designed to study the prompt (simultaneous with gamma radiation) optical emission of gamma-ray bursts and to perform the sky survey to detect unknown objects and transient phenomena. With joint efforts of Sternberg astronomical institute, High altitude astronomical station of the Pulkovo observatory, Ural state university, Irkutsk state university, Blagoveshchensk pedagogical university, the robotic telescopes MASTER II near Kislovodsk, Yekaterinburg, Irkutsk and Blagoveshchensk were installed and tested. The network spread over the longitudes is greater than 6 h. A further expansion of the network is considered. © 2011 Springer Science+Business Media B.V

MASTER Real-Time Multi-Message Observations of High Energy Phenomena

This review considers synchronous and follow-up MASTER Global Robotic Net optical observations of high energy astrophysical phenomena such as fast radio bursts (FRB), gamma-ray bursts (including prompt optical emission polarization discovery), gravitational-wave events, detected by LIGO/VIRGO (including GW170817 and independent Kilonova discovery), high energy neutrino sources (including the detection of IC-170922A progenitor) and others. We report on the first large optical monitoring campaign of the closest at that moment radio burster FRB 180916.J0158+65 simultaneously with a radio burst. We obtained synchronous limits on the optical flux of the FRB 180916.J0158+65 and FRB 200428 (soft gamma repeater SGR 1935+2154) (The CHIME/FRB Collaboration, Nature 2020, 587) at 155093 MASTER images with the total exposure time equal to 2,705,058 s, i.e., 31.3 days. It follows from these synchronous limitations that the ratio of the energies released in the optical and radio ranges does not exceed 4 × 105. Our optical monitoring covered a total of 6 weeks. On 28 April 2020, MASTER automatically following up on a Swift alert began to observe the galactic soft gamma repeater SGR 1935+2154 experienced another flare. On the same day, radio telescopes detected a short radio burst FRB 200428 and MASTER-Tavrida telescope determined the best prompt optical limit of FRB/SGR 1935+2154. Our optical limit shows that X-ray and radio emissions are not explained by a single power-law spectrum. In the course of our observations, using special methods, we found a faint extended afterglow in the FRB 180916.J0158+65 direction associated with the extended emission of the host galaxy

MASTER Real-Time Multi-Message Observations of High Energy Phenomena

This review considers synchronous and follow-up MASTER Global Robotic Net optical observations of high energy astrophysical phenomena such as fast radio bursts (FRB), gamma-ray bursts (including prompt optical emission polarization discovery), gravitational-wave events, detected by LIGO/VIRGO (including GW170817 and independent Kilonova discovery), high energy neutrino sources (including the detection of IC-170922A progenitor) and others. We report on the first large optical monitoring campaign of the closest at that moment radio burster FRB 180916.J0158+65 simultaneously with a radio burst. We obtained synchronous limits on the optical flux of the FRB 180916.J0158+65 and FRB 200428 (soft gamma repeater SGR 1935+2154) (The CHIME/FRB Collaboration, Nature 2020, 587) at 155093 MASTER images with the total exposure time equal to 2,705,058 s, i.e., 31.3 days. It follows from these synchronous limitations that the ratio of the energies released in the optical and radio ranges does not exceed 4 × 105. Our optical monitoring covered a total of 6 weeks. On 28 April 2020, MASTER automatically following up on a Swift alert began to observe the galactic soft gamma repeater SGR 1935+2154 experienced another flare. On the same day, radio telescopes detected a short radio burst FRB 200428 and MASTER-Tavrida telescope determined the best prompt optical limit of FRB/SGR 1935+2154. Our optical limit shows that X-ray and radio emissions are not explained by a single power-law spectrum. In the course of our observations, using special methods, we found a faint extended afterglow in the FRB 180916.J0158+65 direction associated with the extended emission of the host galaxy