scholarly journals A-Statistical Cluster Points in Finite Dimensional Spaces and Application to Turnpike Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Pratulananda Das ◽  
Sudipta Dutta ◽  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
General Notion ◽  
Optimal Controls ◽  
General Version ◽  
Finite Dimensional ◽  
Optimal Paths ◽  
Statistical Cluster ◽  
Turnpike Theorem ◽  
Cluster Points

In the first part of the paper, following the works of Pehlivan et al. (2004), we study the set of allA-statistical cluster points of sequences inm-dimensional spaces and make certain investigations on the set of allA-statistical cluster points of sequences inm-dimensional spaces. In the second part of the paper, we apply this notion to study an asymptotic behaviour of optimal paths and optimal controls in the problem of optimal control in discrete time and prove a general version of turnpike theorem in line of the work of Mamedov and Pehlivan (2000). However, all results of this section are presented in terms of a more general notion ofℐ-cluster points.

scholarly journals Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

scholarly journals Statistical Cluster Points of Sequences in Finite Dimensional Spaces

2004 ◽  
Vol 54 (1) ◽  
pp. 95-102 ◽  
Author(s):  
S. Pehlivan ◽  
A. Güncan ◽  
M. A. Mamedov
Keyword(s):  
Finite Dimensional ◽  
Statistical Cluster ◽  
Cluster Points

scholarly journals Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jiyuan Tan ◽  
Xiangyun Shi ◽  
Zhiheng Li ◽  
Kaidi Yang ◽  
Na Xie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Continuous Time ◽  
Optimal Controls ◽  
Time Model ◽  
Control Plan ◽  
Analytic Proof ◽  
Planning Models ◽  
Gradient Descent Algorithm ◽  
Time Planning

A classical control problem for an isolated oversaturated intersection is revisited with a focus on the optimal control policy to minimize total delay. The difference and connection between existing continuous-time planning models and recently proposed discrete-time planning models are studied. A gradient descent algorithm is proposed to convert the optimal control plan of the continuous-time model to the plan of the discrete-time model in many cases. Analytic proof and numerical tests for the algorithm are also presented. The findings shed light on the links between two kinds of models.

scholarly journals Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abderrahim Labzai ◽  
Abdelfatah Kouidere ◽  
Bouchaib Khajji ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Drug Users ◽  
Control Strategies ◽  
Drug Consumption ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Discrete Mathematical Model

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of drug consumption. The population that we are going to study is divided into six compartments: potential drug users, light drug users, heavy drug users, heavy drug users-dealers and providers, temporary quitters of drug consumption, and permanent quitters of drug consumption. Our objective is to find the best strategy to reduce the number of light drug users, heavy drug users, heavy drug users-dealers and providers, and temporary quitters of drug consumption. We use four control strategies which are awareness programs through media and education, preventing contact through security campaigns, treatment, and psychological support along with follow-up. Pontryagin’s maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the effectiveness of the optimization strategy.

Rough statistical cluster points

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5295-5304
Author(s):  
Salih Aytar
Keyword(s):  
Statistical Convergence ◽  
Cluster Point ◽  
Convergence Criteria ◽  
Finite Dimensional ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Condensation Point ◽  
Statistical Cluster Point ◽  
Dimensional Normed Space ◽  
Cluster Points

In this paper, we define the concepts of rough statistical cluster point and rough statistical limit point of a sequence in a finite dimensional normed space. Then we obtain an ordinary statistical convergence criteria associated with rough statistical cluster point of a sequence. Applying these definitions to the sequences of functions, we come across a new concept called statistical condensation point. Finally, we observe the relations between the sets of statistical condensation points, rough statistical cluster points and rough statistical limit points of a sequence of functions.

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