Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems

2021 ◽  
Vol 34 (5) ◽  
pp. 1703-1722
Author(s):  
George Yin ◽  
Zhexin Wen ◽  
Hongjiang Qian ◽  
Huy Nguyen
Keyword(s):  
Optimal Control ◽  
Numerical Solutions

scholarly journals Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2863
Author(s):  
Napasool Wongvanich ◽  
I-Ming Tang ◽  
Marc-Antoine Dubois ◽  
Puntani Pongsumpun
Keyword(s):  
Optimal Control ◽  
Numerical Solutions ◽  
Foot And Mouth Disease ◽  
Control Policy ◽  
Mouth Disease ◽  
Sensitivity Analyses ◽  
Urban Region ◽  
Control Parameters ◽  
Control Effort ◽  
Logarithmic Relationship

Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time tmax required for the optimal control effort to stay at the maximum amount umax exhibits an intrinsic logarithmic relationship with respect to the control parameters.

Optimal control homotopy perturbation method for cancer model

2019 ◽  
Vol 12 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Perturbation Method ◽  
Cancer Immunotherapy ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Cancer Model ◽  
Homotopy Perturbation

In this paper, we introduced the optimal control homotopy perturbation method (OCHPM) by using the homotopy perturbation method (HPM). Every one, by using of the proposed method, can obtain numerical solutions of mathematical modeling for cancer-immunotherapy. In this paper, in order to prove the preciseness and efficiency of the OCHPM method, we compared the obtained numerical solutions with HPM. The results obtained showed that the OCHPM method is powerful to generate the numerical solutions for some therapeutic models.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

2014 ◽  
Vol 1042 ◽  
pp. 172-177
Author(s):  
Guang Yan Xu ◽  
Ping Li ◽  
Biao Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential Game ◽  
Numerical Solutions ◽  
Game Problem ◽  
Gap Function ◽  
Differential Variational Inequality ◽  
Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

Combined Convection–Conduction–Radiation Boundary Layer Flows Using Optimal Control Penalty Finite Elements

1989 ◽  
Vol 111 (2) ◽  
pp. 433-437 ◽  
Author(s):  
L. R. Utreja ◽  
T. J. Chung
Keyword(s):  
Boundary Layer ◽  
Optimal Control ◽  
Finite Elements ◽  
Optical Thickness ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Boundary Layer Flows ◽  
Combined Convection ◽  
Radiation Boundary ◽  
Plate Geometry

Numerical solutions for combined convection and radiation in a laminar boundary layer on an isothermal wall are obtained using optimal control penalty (OCP) finite elements. The integro-differential energy equation is solved without any limitation of optical thickness. The expression for the divergence of radiation flux containing integral terms is written in terms of a one-dimensional radiation field for a flat plate geometry. The radiation interaction effect on the temperature distribution in the boundary layer is described. The solution of the integro-differential energy equation is then compared with known solutions in the limits of optical thickness.

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