A numerical method for ergodic optimal control of switching diffusions with reflection

The ergodic or long run average cost control problem for diffusions is one of the classical problems of stochastic control that still eludes a completely satisfactory treatment. This is certainly true for the setting in which the systems to be controlled is modeled by the solution of a switching sto...

Full description

Saved in:
Bibliographic Details
Published in:European journal of control 2024-05, Vol.77, p.100989, Article 100989
Main Authors: Leite, Saul C., Fragoso, Marcelo D.
Format: Article
Language:English
Subjects:
Numerical methods
Optimal stochastic control
Switching stochastic differential equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The ergodic or long run average cost control problem for diffusions is one of the classical problems of stochastic control that still eludes a completely satisfactory treatment. This is certainly true for the setting in which the systems to be controlled is modeled by the solution of a switching stochastic differential equation with reflection (SSDER). In this paper, we advance in this rather difficult problem by setting forth preliminary results for the unidimensional case. Besides carving out a numerical method, our treatment of the ergodic control in this scenario straddles issues of existence and uniqueness of solution of the SSDER and a verification theorem for the associated HJB equation. We conclude by illustrating the effectiveness of the method considering the control of energy consumption in a large parallel processing computer system composed of one queue and several processing stations.
ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2024.100989