scholarly journals Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations

2015 ◽  
Vol 53 (2) ◽  
pp. 592-621 ◽  
Author(s):  
Gengsheng Wang ◽  
Yashan Xu ◽  
Yubiao Zhang
Keyword(s):  
Heat Equations ◽  
Optimal Controls ◽  
Time Optimal

scholarly journals Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1956
Author(s):  
Yong Han Kang ◽  
Jin-Mun Jeong
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Stochastic Functional Differential Equations ◽  
Time Optimal ◽  
Target Set ◽  
Functional Differential ◽  
Stochastic Functional

The purpose of this paper is to find the time-optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is to construct a fundamental solution for corresponding linear systems and establish variations of a constant formula of solutions for given stochastic equations. The existence result of time-optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

scholarly journals Free terminal time optimal control problem for the treatment of HIV infection

2016 ◽  
Vol 6 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Amine Hamdache ◽  
Smahane Saadi ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Hiv Infection ◽  
Control Problem ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Terminal Time ◽  
Time Optimal ◽  
Time Optimal Control Problem ◽  
Free Terminal Time

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. The optimal treatment duration and the optimal medications amount are considered. The main objective of this study is to be able to maximize the benet based on number of healthy CD4+ T-cells and CTL immune cells and to minimize the infection level and the overall treatment cost while optimizing the duration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employedto provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.

scholarly journals On the existence of time optimal controls for linear evolution equations

2007 ◽  
Vol 8 (4) ◽  
pp. 925-941 ◽  
Author(s):  
Kim Dang Phung ◽  
◽  
Gengsheng Wang ◽  
Xu Zhang ◽  
◽  
...  
Keyword(s):  
Evolution Equations ◽  
Optimal Controls ◽  
Linear Evolution ◽  
Time Optimal ◽  
Linear Evolution Equations
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