High-order numerical solutions to Bellman's equation of optimal control

2012 ◽  
Author(s):  
C. O. Aguilar ◽  
A. J. Krener
Keyword(s):  
Optimal Control ◽  
Numerical Solutions ◽  
High Order ◽  
Bellman's Equation ◽  
Bellman’S Equation

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.

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
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