Optimality on Homogeneous Spaces, and the Angle System Associated with a Bilinear Control System

2009 ◽  
Vol 48 (4) ◽  
pp. 2636-2650 ◽  
Author(s):  
V. Ayala ◽  
J. C. Rodríguez ◽  
L. A. B. San Martin
Keyword(s):  
Control System ◽  
Homogeneous Spaces ◽  
Bilinear Control

Study of Controllability of Bilinear Systems with Limited Control

2021 ◽  
Vol 26 (3-4) ◽  
pp. 302-313
Author(s):  
L.G. Gagarina ◽  
◽  
A.A. Doronina ◽  
R.A. Fomin ◽  
D.A. Chukhlyaev ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Control Systems ◽  
Control Program ◽  
Bilinear System ◽  
Equation System ◽  
Bilinear Systems ◽  
Complete Controllability ◽  
Complex Objects ◽  
Bilinear Control

Optimal control is closely related to the choice of the most advantageous control modes for complex objects, which are described using ordinary differential systems. The problem of optimal control consists in calculating the optimal control program and synthesizing the optimal control system. This problem arises in the applied field of the optimal control theory, in the case when control is based on the principle of feedback and in automatic control systems. Optimal control problems, as a rule, are calculated by numerical methods to find the extremum of a functional or to solve a boundary value problem for a differential equation system. From a mathematical standpoint, the synthesis of optimal control systems is a nonlinear programming problem in functional spaces. In this study the problem of complete controllability of a bilinear control system on the plane was considered. The controllability of bilinear systems with both unlimited and limited control was studied. The evidences of closed trajectory systems controllability theorems were produced. The authors have defined multiple criteria of complete controllability for bilinear system with limited control. The complete controllability conditions of bilinear control system have been proposed with their algebraic reasoning. In the contemporary context of universal robotization of production, completely controllable systems matter in navigation, as well as in modeling of a number of economic and social processes.

scholarly journals On the Optimal Stabilisation for a set of Programmed Motions of the Bilinear Control System

PAMM ◽  
2003 ◽  
Vol 2 (1) ◽  
pp. 100-101 ◽  
Author(s):  
N. V. Smirnov ◽  
T. E. Smirnov
Keyword(s):  
Control System ◽  
Bilinear Control

A controller for safe, convenient operation of LaB6 emitters on electron-beam instruments

1983 ◽  
Vol 41 ◽  
pp. 408-409
Author(s):  
W. J. Abramson ◽  
H. W. Estry ◽  
L. F. Allard
Keyword(s):  
Electron Beam ◽  
Control System ◽  
Thermal Shock ◽  
Appropriate Care ◽  
Electron Guns ◽  
Tungsten Filaments ◽  
Order Of Magnitude ◽  
Main Components

LaB6 emitters are becoming increasingly popular as direct replacements for tungsten filaments in the electron guns of modern electron-beam instruments. These emitters offer order of magnitude increases in beam brightness, and, with appropriate care in operation, a corresponding increase in source lifetime. They are, however, an order of magnitude more expensive, and may be easily damaged (by improper vacuum conditions and thermal shock) during saturation/desaturation operations. These operations typically require several minutes of an operator's attention, which becomes tedious and subject to error, particularly since the emitter must be cooled during sample exchanges to minimize damage from random vacuum excursions. We have designed a control system for LaBg emitters which relieves the operator of the necessity for manually controlling the emitter power, minimizes the danger of accidental improper operation, and makes the use of these emitters routine on multi-user instruments.Figure 1 is a block schematic of the main components of the control system, and Figure 2 shows the control box.

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