An optimal control problem without control costs

A two-dimensional diffusion process is controlled until it enters a given subset of $ \mathbb{R}^2 $. The aim is to find the control that minimizes the expected value of a cost function in which there are no control costs. The optimal control can be expressed in terms of the value function, which gi...

Full description

Saved in:
Bibliographic Details
Published inMathematical biosciences and engineering : MBE Vol. 20; no. 3; pp. 5159 - 5168
Main Author Lefebvre, Mario
Format Journal Article
LanguageEnglish
Published United States AIMS Press 01.01.2023
Subjects
diffusion processes
dynamic programming
first-passage time
partial differential equation
stochastic optimal control
stochastic optimal control
dynamic programming
diffusion processes
partial differential equation
first-passage time
Online AccessGet full text

Cover

More Information
Summary:A two-dimensional diffusion process is controlled until it enters a given subset of $ \mathbb{R}^2 $. The aim is to find the control that minimizes the expected value of a cost function in which there are no control costs. The optimal control can be expressed in terms of the value function, which gives the smallest value that the expected cost can take. To obtain the value function, one can make use of dynamic programming to find the differential equation it satisfies. This differential equation is a non-linear second-order partial differential equation. We find explicit solutions to this non-linear equation, subject to the appropriate boundary conditions, in important particular cases. The method of similarity solutions is used.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1551-0018
1551-0018
DOI:10.3934/mbe.2023239