scholarly journals Fully Coupled Forward-Backward Stochastic Functional Differential Equations and Applications to Quadratic Optimal Control

2020 ◽  
Vol 33 (6) ◽  
pp. 1886-1902
Author(s):  
Xiaoming Xu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Quadratic Optimal Control ◽  
Functional Differential ◽  
Fully Coupled ◽  
Stochastic Functional

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 Time Optimal Control for Semilinear Stochastic Functional Differential Equations With Delays

2021 ◽  
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 construct a fundamental solution for corresponding linear systems and establish variations of 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.

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