A method of approximate reachable set construction on the plane for a bilinear control system with uncertainty

2018 ◽  
Author(s):  
A. R. Matviychuk ◽  
O. G. Matviychuk
Keyword(s):  
Control System ◽  
Reachable Set ◽  
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
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