scholarly journals A Model Problem for Optimal Control of a Parabolic PDE Fully Coupled to ODEs

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Sven-Joachim Kimmerle
Keyword(s):  
Optimal Control ◽  
Model Problem ◽  
Parabolic Pde ◽  
Fully Coupled

scholarly journals Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Min ◽  
Ying Peng ◽  
Yongli Qin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Maximum Principles ◽  
Control Problems ◽  
Linear Quadratic Optimal Control ◽  
Fully Coupled

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

scholarly journals On a Class of Forward-Backward Stochastic Differential Systems in Infinite Dimensions

2007 ◽  
Vol 2007 ◽  
pp. 1-33 ◽  
Author(s):  
Giuseppina Guatteri
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Stochastic Optimal Control ◽  
Large Time ◽  
Regularity Property ◽  
Time Interval ◽  
Infinite Dimensions ◽  
Differential Systems ◽  
Stochastic Optimal Control Problem ◽  
Fully Coupled

We prove that a class of fully coupled forward-backward systems in infinite dimensions has a local unique solution. After studying the regularity property of the solution, we prove that for a peculiar class of systems arising in the theory of stochastic optimal control, the solution exists in arbitrary large time interval. Finally, we investigate the connection between the solution to the systems and a stochastic optimal control problem.

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