scholarly journals Feedback stabilization for a bilinear control system under weak observability inequalities

Automatica ◽  
2020 ◽  
Vol 113 ◽  
pp. 108821
Author(s):  
Kaïs Ammari ◽  
Mohamed Ouzahra
Keyword(s):  
Control System ◽  
Feedback Stabilization ◽  
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.

Feedback stabilization of tokamaks against slow axisymmetric MHD instabilities

1981 ◽  
Vol 26 (2) ◽  
pp. 351-357 ◽  
Author(s):  
Torkil H. Jensen
Keyword(s):  
Growth Rate ◽  
Control System ◽  
Stability Analysis ◽  
Vacuum Chamber ◽  
Feedback Stabilization ◽  
Wall Material ◽  
Growth Time ◽  
Conducting Wall ◽  
Mhd Instabilities ◽  
The Stability

Single axis tokamaks as well as doublets may be unstable toward axisymmetric MHD instabilities. Such instabilities may, for the case of a single-axis tokamak, be slow when the plasma is surrounded by a relatively close fitting conducting wall, such as a vacuum chamber; the growth rate may be proportional to the resistivity of the wall material. For the case of doublets, slowly growing instabilities with growth rates proportional to the plasma resistivity exist. Such slow instabilities can be stabilized by feedback control of the currents through coils surrounding the plasma; since it is only required that the amplifiers used in the circuits respond fast compared with the growth time of the slow instabilities, this feedback stabilization is not technologically demanding. This paper describes a formalism for the stability analysis of such a system consisting of the plasma, surrounded by a conducting wall or vacuum chamber and coils with their control system.

scholarly journals Stability and Feedback Stabilization of HIV Infection Model with Two Classes of Target Cells

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
A. M. Elaiw ◽  
A. M. Shehata
Keyword(s):  
Control System ◽  
Steady State ◽  
Hiv Infection ◽  
Highly Active Antiretroviral Therapy ◽  
Feedback Stabilization ◽  
Infection Model ◽  
Target Cells ◽  
Control Input ◽  
Time Model ◽  
Hiv Infection Model

We study the stability and feedback stabilization of the uninfected steady state of a human immunodeficiency virus (HIV) infection model. The model is a 6-dimensional nonlinear ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages, and takes into account the Cytotoxic T Lymphocytes (CTLs) immune response. Lyapunov function is constructed to establish the global asymptotic stability of the uninfected steady state of the model. In a control system framework, the HIV infection model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is considered as a nonlinear control system with drug dose as control input. We developed treatment schedules for HIV-infected patients by using Model Predictive Control (MPC-)based method. The MPC is constructed on the basis of an approximate discrete-time model of the HIV infection model. The MPC is applied to the stabilization of the uninfected steady state of the HIV infection model. Besides model inaccuracies that HIV infection model suffers from, some disturbances/uncertainties from different sources may arise in the modelling. In this work the disturbances are modelled in the HIV infection model as additive bounded disturbances. The robustness of the MPC against small model uncertainties or disturbances is also shown.

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