scholarly journals Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester(n,1)Attrition Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Ancai Zhang
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Dynamic Systems ◽  
Control Strategies ◽  
Discrete Event ◽  
Optimal Strategies ◽  
Hybrid Dynamic System ◽  
Differential Game Theory ◽  
Case Simulation ◽  
Lanchester Equation

For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a(n,1)battle, where a heterogeneous force ofndifferent troop types faces a homogeneous force. This model can be characterized by the interaction of continuous-time models (governed by Lanchester equation), and discrete event systems (described by variable tactics). Furthermore, an expository discussion is presented on an optimal variable tactics control problem for warfare hybrid dynamic system. The optimal control strategies are designed based on dynamic programming and differential game theory. As an example of the consequences of this optimal control problem, we take the (2, 1) case and solve the optimal strategies in a (2, 1) case. Simulation results show the feasibility of warfare hybrid system model and the effectiveness of the optimal control strategies designed.

scholarly journals Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baba Seidu ◽  
Oluwole D. Makinde
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Nonlinear Dynamical ◽  
Basic Model ◽  
Hiv Aids

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number,R0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated whenR0<1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

Linear optimal control strategies for production systems with a discrete-event demand pattern

2012 ◽  
Vol 24 (3) ◽  
pp. 339-352
Author(s):  
Davide Giglio ◽  
Riccardo Minciardi ◽  
Simona Sacone ◽  
Silvia Siri
Keyword(s):  
Optimal Control ◽  
Production Systems ◽  
Control Strategies ◽  
Discrete Event ◽  
Linear Optimal Control ◽  
Demand Pattern

Optimal Vaccination of an Endemic Model with Variable Infectivity and Infinite Delay

2013 ◽  
Vol 68 (10-11) ◽  
pp. 677-685 ◽  
Author(s):  
Gul Zaman ◽  
Yasuhisa Saito ◽  
Madad Khan
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Control Function ◽  
Control Strategies ◽  
Infinite Delay ◽  
Nonlinear Differential Equations ◽  
Infected Individual ◽  
Vaccination Schedule ◽  
Disease Evolution ◽  
Spread Of Infection

In this work, we consider a nonlinear SEIR (susceptible, exposed, infectious, and removed) endemic model, which describes the dynamics of the interaction between susceptible and infected individuals in a population. The model represents the disease evolution through a system of nonlinear differential equations with variable infectivity which determines that the infectivity of an infected individual may not be constant during the time after infection. To control the spread of infection and to find a vaccination schedule for an endemic situation, we use optimal control strategies which reduce the susceptible, exposed, and infected individuals and increase the total number of recovered individuals. In order to do this, we introduce the optimal control problem with a suitable control function using an objective functional. We first show the existence of an optimal control for the control problem and then derive the optimality system. Finally the numerical simulations of the model is identified to fit realistic measurement which shows the effectiveness of the model.

scholarly journals Optimal Control Problem for Cholera Disease and Cost-Effectiveness Analysis

2021 ◽  
Vol 53 (2) ◽  
pp. 200-2017
Author(s):  
Jhoana Patricia Romero-Leiton ◽  
Muhammad Ozair ◽  
Takasar Hussaing
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Cost Effectiveness Analysis ◽  
Effectiveness Analysis ◽  
Using Data ◽  
Theoretical Results

Cholera is a disease that continues to be a threat to public health globally and is an indicator of inequity and lack of social development in countries. For this reason, strategies for its control need to be investigated. In this work, an optimal control problem related to cholera disease was formulated by introducing personal protection, drug treatment and water sanitation as control strategies. First, the existence and characterization of controls to minimize the performance index or cost function was proved by using classic control theory. Then, the theoretical results were validated with numerical experiments by using data reported in the literature. Finally, the effectiveness and efficiency of the proposed controls were determined through a cost-effectiveness analysis. The results showed that the use of the three controls simultaneously is the cheapest and most effective strategy to control the disease.

scholarly journals Optimization of spatial control strategies for population replacement, application to Wolbachia

2021 ◽  
Author(s):  
Yannick Privat ◽  
Michel Duprez ◽  
Nicolas Vauchelet ◽  
Romane Hélie
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Mosquito Population ◽  
Infected Mosquito ◽  
Asymptotic Model ◽  
Population Replacement ◽  
Replacement Technique ◽  
Very High

In this article, we are interested in the analysis and simulation of solutions to an optimal control problem motivated by population dynamics issues. In order to control the spread of mosquito-borne arboviruses, the population replacement technique consists in releasing into the environment mosquitoes infected with the Wolbachia bacterium, which greatly reduces the trans- mission of the virus to the humans. Spatial releases are then sought in such a way that the infected mosquito population invades the uninfected mosquito population. Assuming very high mosquito fecundity rates, we first introduce an asymptotic model on the proportion of infected mosquitoes and then an optimal control problem to determine the best spatial strategy to achieve these releases. We then analyze this problem, including the optimality of natural candidates and carry out first numerical simulations in one dimension of space to illustrate the relevance of our approach.

scholarly journals Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Initial Conditions ◽  
Control Strategies ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Optimal Controls ◽  
Modeling And Control ◽  
Partial Rank Correlation ◽  
Objective Functional

In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters.

scholarly journals Optimal control problem on COVID-19 disease transmission model considering medical mask, disinfectants and media campaign

2020 ◽  
Vol 202 ◽  
pp. 12009
Author(s):  
Dipo Aldila
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Disease Transmission ◽  
Control Strategies ◽  
Population Based ◽  
Transmission Model ◽  
Media Campaign ◽  
Free Virus ◽  
Final State

In this paper, a system of ordinary differential equation approach is developed to understand the spread of COVID-19. We first formulate the dynamic model by dividing the human population based on their health status, awareness status, and also including the free virus on the environment. We provide a basic analysis of the model regarding the well-posed properties and how the basic reproduction number can be used to determine the final state of COVID-19 in the population. A Pontryagin Maximum’s Principle used to construct the model as an optimal control problem in a purpose to determine the most effective strategies against the spread of COVID-19. Three control strategies involved in the model, such as media campaign to develop an awareness of individuals, medical masks to prevent direct transmission, and use of disinfectant to reduce the number of free virus in the environment. Through numerical simulations, we find that the time-dependent control succeeds in reducing the outbreak of COVID-19. Furthermore, if the intervention should be implemented as a single intervention, then the media campaign gives the most effective cost strategy.

scholarly journals Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Purity Ngina ◽  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi
Keyword(s):  
Optimal Control ◽  
Deterministic Model ◽  
Control Strategies ◽  
Treatment Strategies ◽  
Optimal Strategies ◽  
Hiv Treatment ◽  
Sub Saharan Africa ◽  
System Control ◽  
Hiv Dynamics

HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin’s Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.

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