scholarly journals On Optimal Control Problem for Backward Stochastic Doubly Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Adel Chala
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Diffusion Coefficient ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
State Equation ◽  
Control Problems ◽  
Sufficient Condition ◽  
Doubly Stochastic

We are going to study an approach of optimal control problems where the state equation is a backward doubly stochastic differential equation, and the set of strict (classical) controls need not be convex and the diffusion coefficient and the generator coefficient depend on the terms control. The main result is necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

scholarly journals Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint

2004 ◽  
Vol 46 (2) ◽  
pp. 171-184
Author(s):  
Mi Jin Lee ◽  
Jong Yeoul Park
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Pontryagin’S Maximum Principle ◽  
State Constraint ◽  
Parabolic Differential Equation ◽  
Control Problems ◽  
Pontryagin's Maximum Principle ◽  
Well Posed

AbstractIn this paper, we study Pontryagin's maximum principle for some optimal control problems governed by a non-well-posed parabolic differential equation. A new penalty functional is applied to derive Pontryagin's maximum principle and an application for this system is given.

scholarly journals Stochastic maximum principle for optimal control problem of forward and backward system

1995 ◽  
Vol 37 (2) ◽  
pp. 172-185 ◽  
Author(s):  
Wensheng Xu
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Stochastic Systems ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
State Variables ◽  
The Maximum Principle

AbstractThe maximum principle for optimal control problems of stochastic systems consisting of forward and backward state variables is proved, under the assumption that the diffusion coefficient does not contain the control variable, but the control domain need not be convex.

scholarly journals A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems

2021 ◽  
Author(s):  
Christelle Dleuna Nyoumbi ◽  
Antoine Tambue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Finite Difference Method ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Hjb Equation ◽  
High Dimensional ◽  
Control Problems ◽  
Volume Method

AbstractStochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton–Jacobi–Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the only tools to provide accurate approximations. The aims of this paper is to introduce a novel fitted finite volume method to solve high dimensional degenerated HJB equation from stochastic optimal control problems in high dimension ($$ n\ge 3$$ n ≥ 3 ). The challenge here is due to the nature of our HJB equation which is a degenerated second-order partial differential equation coupled with an optimization problem. For such problems, standard scheme such as finite difference method losses its monotonicity and therefore the convergence toward the viscosity solution may not be guarantee. We discretize the HJB equation using the fitted finite volume method, well known to tackle degenerated PDEs, while the time discretisation is performed using the Implicit Euler scheme.. We show that matrices resulting from spatial discretization and temporal discretization are M-matrices. Numerical results in finance demonstrating the accuracy of the proposed numerical method comparing to the standard finite difference method are provided.

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