Weakly Coercive Problems in Nonlinear Stochastic Control: Existence of Optimal Controls

2010 ◽  
Vol 48 (5) ◽  
pp. 3532-3561 ◽  
Author(s):  
M. Motta ◽  
C. Sartori
Keyword(s):  
Stochastic Control ◽  
Optimal Controls ◽  
Existence Of Optimal Controls ◽  
Coercive Problems

On the Existence of Optimal Controls

1962 ◽  
Vol 84 (1) ◽  
pp. 13-20 ◽  
Author(s):  
L. Markus ◽  
E. B. Lee
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Optimal Controls ◽  
Optimum Control ◽  
Existence Of Optimal Controls ◽  
Differential Equation Models ◽  
Controlling Processes

The problem of existence of various types of optimum controls for controlling processes which are described by ordinary differential equation models is considered. The results presented enable one to test if there does exist an optimum control in the class of controls under consideration before proceeding to the construction of an optimal control.

Existence of optimal controls for systems of controlled forward-backward doubly SDEs

2020 ◽  
Vol 28 (2) ◽  
pp. 93-112
Author(s):  
Abdelhakim Ninouh ◽  
Boulakhras Gherbal ◽  
Nassima Berrouis
Keyword(s):  
Weak Convergence ◽  
Control Problem ◽  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Optimal Controls ◽  
Convexity Condition ◽  
Relaxed Controls ◽  
Relaxed Control ◽  
Doubly Stochastic ◽  
Existence Of Optimal Controls

AbstractWe wish to study a class of optimal controls for problems governed by forward-backward doubly stochastic differential equations (FBDSDEs). Firstly, we prove existence of optimal relaxed controls, which are measure-valued processes for nonlinear FBDSDEs, by using some tightness properties and weak convergence techniques on the space of Skorokhod {\mathbb{D}} equipped with the S-topology of Jakubowski. Moreover, when the Roxin-type convexity condition is fulfilled, we prove that the optimal relaxed control is in fact strict. Secondly, we prove the existence of a strong optimal controls for a linear forward-backward doubly SDEs. Furthermore, we establish necessary as well as sufficient optimality conditions for a control problem of this kind of systems. This is the first theorem of existence of optimal controls that covers the forward-backward doubly systems.

Existence of optimal controls for systems driven by FBSDEs

2011 ◽  
Vol 60 (5) ◽  
pp. 344-349 ◽  
Author(s):  
Khaled Bahlali ◽  
Boulekhrass Gherbal ◽  
Brahim Mezerdi
Keyword(s):  
Optimal Controls ◽  
Existence Of Optimal Controls
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