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.

scholarly journals Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 749-757
Author(s):  
Ali Safari ◽  
Yagub Sharifov ◽  
Yusif Gasimov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlocal Conditions ◽  
Integral Boundary Conditions ◽  
Necessary Optimality Condition ◽  
Integral Boundary ◽  
Singular Controls ◽  
The Cauchy Problem ◽  
Continue Investigation

In this paper, we continue investigation of the problem considered in our earlier works. The paper deals with an optimal control problem for an ordinary differential equation with integral boundary conditions that generalizes the Cauchy problem. The problem is investigated the case when Pontryagin?s maximum principle is degenerate. Moreover, the second order optimality conditions are derived for the considered problem.

scholarly journals A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

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 Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Xueping Zhu ◽  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Horizon ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic delay evolution equation in Hilbert spaces. The existence and uniqueness of the optimal control are obtained by means of associated infinite horizon backward stochastic differential equations without assuming the Gâteaux differentiability of the drift coefficient and the diffusion coefficient. An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.

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 SYARAT CUKUP UNTUK OPTIMALITAS MASALAH KONTROL KUADRATIK LINIER

2013 ◽  
Vol 2 (2) ◽  
pp. 63
Author(s):  
Suci Fratama Sari
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Riccati Equation ◽  
Existence And Uniqueness ◽  
Algebraic Riccati Equation ◽  
Lqr Problem ◽  
Existence Of Optimal Control

The LQR problem is an optimal control problem which is now used in variouselds of science. The optimal control is given by u(t) = 􀀀Kx(t), where K = R􀀀1(PB)Tand P is a unique positive semidenite solution of Algebraic Riccati Equation (ARE).The existence of optimal control u(t) depends on the existence matrix P. In this paper,the sucient conditions which ensures the existence and uniqueness of the optimal con-trol u(t) will be determined. Moreover, some examples as an illustration of the LQRproblem will be given.

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