Interval optimal control problem in a Hilbert space

2013 ◽  
Vol 53 (4) ◽  
pp. 389-395 ◽  
Author(s):  
O. Victoria Olegovna
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Optimal Control Problem ◽  
Control Problem

scholarly journals Stochastic differential equations in infinite dimensional Hilbert space and its optimal control problem with Lévy processes

2021 ◽  
Vol 7 (2) ◽  
pp. 2427-2455
Author(s):  
Meijiao Wang ◽  
◽  
Qiuhong Shi ◽  
Maoning Tang ◽  
Qingxin Meng ◽  
...  
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Teugels Martingales

<abstract><p>The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugels martingales which are more general processes and the corresponding optimal control problems. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens <sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup>). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classic convex variation method and dual techniques. The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.</p></abstract>

scholarly journals Optimal problem of cost function for the linear neutral systems

2001 ◽  
Vol 25 (12) ◽  
pp. 777-785
Author(s):  
Jong Yeoul Park ◽  
Yong Han Kang
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cost Function ◽  
Optimal Condition ◽  
Neutral Type ◽  
Neutral Systems ◽  
Quadratic Cost ◽  
Quadratic Cost Function

We study the optimal control problem of a system governed by linear neutral type in Hilbert spaceX. We investigate optimal condition for quadratic cost function and as applications, we give some examples.

scholarly journals Stochastic Differential Equations in Infinite Dimensional Hilbert Space and its Optimal Control Problem with L´evy Processes

2021 ◽  
Author(s):  
Meijiao Wang ◽  
Qiuhong Shi ◽  
Qingxin Meng ◽  
Maoning Tang
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Teugels Martingales

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

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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