View Item 

A class of optimal state-delay control problems

Access Status
Open access
Authors
Chai, Q.
Loxton, Ryan
Teo, Kok Lay (ah Nge)
Yang, C.
Date
2013
Type
Journal Article

Metadata
Show full item record
Citation
Chai, Qinqin and Loxton, Ryan and Teo, Kok Lay and Yang, Chunhua. 2013. A class of optimal state-delay control problems. Nonlinear Analysis: Real World Applications. 14 (2013): pp. 1536-1550.
Source Title
Nonlinear Analysis: Real World Applications
DOI
ISSN
Remarks

NOTICE: This is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Real World Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Real World Applications, Vol. 14 (2013). doi: 10.1016/j.nonrwa.2012.10.017

URI
Collection
Abstract

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem – called an optimal state-delay control problem – that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.