The Nonautonomous Linear Oskolkov Model on a Geometrical Graph: The Stability of Solutions and the Optimal Control Problem

2014 ◽  
pp. 257-271 ◽  
Author(s):  
Minzilia A. Sagadeeva ◽  
Georgy A. Sviridyuk
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stability Of Solutions ◽  
Geometrical Graph ◽  
The Stability

scholarly journals Stabilization and Analytic Approximate Solutions of an Optimal Control Problem

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 476-487 ◽  
Author(s):  
Camelia Pop ◽  
Camelia Petrişor ◽  
Remus-Daniel Ene
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Equilibrium Points ◽  
Approximate Solutions ◽  
Linear Control ◽  
Runge Kutta Method ◽  
The Stability ◽  
Stability Results

Abstract This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) × ℝ3 × ℝ3 in deep connection with the important role of the Lie groups in tackling the various problems occurring in physics, mathematics, engineering and economic areas [1, 2, 3, 4, 5]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [6]), so a linear control has been considered in order to stabilize the dynamics. The analytic approximate solutions of the resulting nonlinear system are established and a comparison with the numerical results obtained via the fourth-order Runge-Kutta method is achieved.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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