By Topic

Numerical methods for the optimization of nonlinear stochastic delay systems, and an application to internet regulation

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Kushner, H.J. ; Appl. Math, Brown Univ., Providence, RI, USA

The Markov chain approximation method is an effective and widely used approach for computing optimal values and controls for stochastic systems. It was extended to nonlinear (and possibly reflected) diffusions with delays in a recent book. The path, control, and reflection terms can all be delayed. In models of communications systems, reflection terms correspond to buffer overflows, and to the adjustments needed to keep the buffers and rates nonnegative and bounded. The book concentrated on convergence proofs for general algorithms of promising forms. If the control and/or reflection terms are delayed, the memory requirements can make the problem intractable, since these have little or no regularity. For such models, the problem was recast in terms of a “wave” or “transportation” equation, to get practical algorithms with very much reduced computational needs. The overall approach to getting usable algorithms is outlined. The methods are applied to an ideal model of a communications system with transportation delay. and it is seen that nearly optimal controls for appropriately chosen criteria can improve the performance considerably and be robust in the face of changing operating conditions. The data illustrate the potential usefulness of numerical methods for nonlinear stochastic systems with delays. It opens up new avenues of control for consideration.

Published in:

Decision and Control (CDC), 2010 49th IEEE Conference on

Date of Conference:

15-17 Dec. 2010