On the role of optimality functions in numerical optimal control

2011 ◽  
Vol 35 (2) ◽  
pp. 247-253 ◽  
Author(s):  
Elijah Polak
Keyword(s):  
Optimal Control ◽  
Optimality Functions

Role of pine wilt disease based on optimal control strategy at multiple scales: A case study of Korea

2021 ◽  
Vol 46 (4) ◽  
Author(s):  
Muhammad Ozair ◽  
Takasar Hussain ◽  
Kashif Ali Abro ◽  
Sajid Jameel ◽  
Aziz Ullah Awan
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Multiple Scales ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Optimal Control Strategy ◽  
Pine Wilt

Optimality and Taylor Rules

2000 ◽  
Vol 174 ◽  
pp. 80-91 ◽  
Author(s):  
Andrew P. Blake
Keyword(s):  
Optimal Control ◽  
Taylor Rule ◽  
Taylor Rules ◽  
Forward Looking

This paper discusses the role of forecasts in the control of inflation. Much has been made of variations on the so-called Taylor rule for inflation control. Forward-looking Taylor rules are reconciled with optimal control using a class of rules described as error-correcting Taylor rules.

scholarly journals Optimal Control Strategy for SEIR with Latent Period and a Saturated Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Abta Abdelhadi ◽  
Laarabi Hassan
Keyword(s):  
Optimal Control ◽  
Latent Period ◽  
Incidence Rate ◽  
Nonlinear Model ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Vaccination Strategies ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

We propose an SEIR epidemic model with latent period and a modified saturated incidence rate. This work investigates the fundamental role of the vaccination strategies to reduce the number of susceptible, exposed, and infected individuals and increase the number of recovered individuals. The existence of the optimal control of the nonlinear model is also proved. The optimality system is derived and then solved numerically using a competitive Gauss-Seidel-like implicit difference method.

scholarly journals Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 893 ◽  
Author(s):  
Andreea Bejenaru ◽  
Constantin Udriste
Keyword(s):  
Optimal Control ◽  
Formal Analysis ◽  
Linear Connection ◽  
Riemannian Structure ◽  
State Variables ◽  
Riemann Curvature Tensor ◽  
Local Coordinates ◽  
Geometric Elements ◽  
Cost Functionals

This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

A STRATEGY OF OPTIMAL EFFICACY OF T11 TARGET STRUCTURE IN THE TREATMENT OF BRAIN TUMOR

2019 ◽  
Vol 27 (02) ◽  
pp. 225-255 ◽  
Author(s):  
SUBHAS KHAJANCHI ◽  
SANDIP BANERJEE
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Transforming Growth Factor ◽  
Treatment Strategies ◽  
Target Structure ◽  
Optimal Control Strategy ◽  
Immunosuppressive Cytokine ◽  
Quadratic Optimal Control ◽  
The Mathematical Model

We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-lymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-[Formula: see text] (TGF-[Formula: see text]), immunostimulatory cytokine interferon-[Formula: see text] (IFN-[Formula: see text]) and the concentrations of immunotherapeutic agent T11TS. For the better understanding of the circumstances under which the gliomas can be eradicated from a patient, we use optimal control strategy. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximizes the macrophages and activated CTLs. The existence and the characterization for the optimal control are established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11TS reduce the glioma burden and increase the cell count of activated CTLs and macrophages.

ROLE OF MEDIA COVERAGE IN MITIGATING AN EPIDEMIC OUTBREAK: AN OPTIMAL CONTROL MODEL

2021 ◽  
pp. 1-24
Author(s):  
ANSHIKA KAPOOR ◽  
ANIRUDDHA DEKA ◽  
SAMIT BHATTACHARYYA
Keyword(s):  
Public Health ◽  
Optimal Control ◽  
Vaccination Coverage ◽  
Disease Transmission ◽  
Media Coverage ◽  
Public Health Department ◽  
Total Cost ◽  
Functional Relationships ◽  
The Cost

Flu is an acute respiratory infection caused by the influenza virus. The outbreak usually occurs every year in temperate region during the fall and winter seasons, but it is present year-round in tropics. Perceived risk of infection, affordability and lack of awareness among the population results in a low level of vaccination coverage. To control disease transmission and promote vaccination, public health officials use media coverage to spread awareness on vaccine safety, vaccine coverage, disease prevalence in the population through public health websites, advertisements, and other social media web pages. Media coverage acts as an incentive as it helps to decrease overall transmission potential and also at the same time increases the vaccination coverage in the population. Since the public health department has a limited budget, it needs to make optimum allocation of its effort to reduce the total cost of infection. Our paper investigates the effect of media coverage using SIR model of disease transmission. We look at three possible functional relationships — linear, exponential, and hyperbolic — the way media coverage may affect the disease transmission and vaccination rate. We derive necessary conditions of optimal solution using Optimal Control Theory and Pontryagin Maximum Principle (PMP) to minimize the total cost for infection. Analysis of our paper demonstrates that the cost of optimal management is four times less than the cost of constant control effort, and putting more effort into reducing transmission is optimal rather than an effort to increase vaccination at the beginning of the outbreak. Analysis of the role of media coverage under three different scenarios may help in formulating policies for public health programs in mitigating the influenza outbreak.

scholarly journals Regularized optimal control problem for a beam vibrating against an elastic foundation

2015 ◽  
Vol 63 (1) ◽  
pp. 53-71
Author(s):  
Igor Bock ◽  
Mária Kečkemétyová
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Foundation ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value

Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a clamped beam against a u elastic foundation. A variable thickness of a beam plays the role of a control variable. The original equation for the deflection is regularized in order to derive necessary optimality conditions

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