Theoretical Fundamentals for Unimodality Estimation of an Objective Functional in the Optimal Control Problem

2019 ◽  
Author(s):  
Askhat I. Diveev ◽  
Elizaveta Yu. Shmalko ◽  
Elena A. Sofronova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Objective Functional

scholarly journals Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Kaifan Huang ◽  
Pengdeng Li ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Negative Impact ◽  
Cost Effective ◽  
Control Approach ◽  
Novel Virus ◽  
Optimality Systems ◽  
Objective Functional ◽  
Optimal Control Approach

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

scholarly journals Energy-Efficient Patching Strategy for Wireless Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (2) ◽  
pp. 262 ◽  
Author(s):  
Pengdeng Li ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Xiang Zhong ◽  
Junhao Wen ◽  
...  
Keyword(s):  
Optimal Control ◽  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Energy Efficient ◽  
Original Problem ◽  
Wireless Sensor ◽  
Virus Attack ◽  
Objective Functional

Wireless sensor networks (WSNs) are vulnerable to computer viruses. To protect WSNs from virus attack, the virus library associated with each sensor node must be updated in a timely way. This article is devoted to developing energy-efficient patching strategies for WSNs. First, we model the original problem as an optimal control problem in which (a) each control stands for a patching strategy, and (b) the objective functional to be optimized stands for the energy efficiency of a patching strategy. Second, we prove that the optimal control problem is solvable. Next, we derive the optimality system for solving the optimal control problem, accompanied with a few examples. Finally, we examine the effects of some factors on the optimal control. The obtained results help improve the security of WSNs.

scholarly journals BILINEAR OPTIMAL CONTROL OF THE VELOCITY TERM IN A VON KÁRMÁN PLATE EQUATION

2013 ◽  
Vol 54 (4) ◽  
pp. 291-305
Author(s):  
JONG YEOUL PARK ◽  
SUN HYE PARK ◽  
YONG HAN KANG
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence Of Solutions ◽  
Plate Equation ◽  
Spatial Variables ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Von Kármán ◽  
Objective Functional

AbstractWe consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

scholarly journals An optimal control problem with final observation for systems governed by nonlinear Schrödinger equation

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 649-665 ◽  
Author(s):  
Aksoy Yildirim ◽  
Eray Aksoy ◽  
Yusuf Kocak
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Necessary Optimality Condition ◽  
Uniqueness Of The Solution ◽  
Variational Form ◽  
Final Observation ◽  
The First Variation ◽  
Objective Functional

In this paper, an optimal control problem with final observation for systems governed by nonlinear time-dependent Schr?dinger equation is studied. The existence and uniqueness of the solution of considered optimal control problem are proved. The first variation of objective functional is obtained and a necessary optimality condition in the variational form is given.

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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