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Toward a More Efficient Implementation of Distributed-Delay Elements

Troeng, Olof LU and Mirkin, Leonid (2013) 52nd IEEE Conference on Decision and Control, 2013 p.294-299
Abstract
This note studies lumped-delay approximations of distributed-delay elements arising in various problems involving delay compensation or preview utilization. Several approaches to reduce implementation complexity, understood as the number of delays required to attain a required accuracy level, are put forward. First, we derive the H2-optimal coefficients for a given delay pattern. This can be seen as a problem-oriented alternative to traditionally used Newton-Cotes numerical integration rules. Second, we propose a computationally efficient method for finding the H2-optimal delay pattern, which uses dynamic programming on multistage graphs. Third, we propose a convex optimization approach, based on ℓ1 heuristics, of reducing the number of... (More)
This note studies lumped-delay approximations of distributed-delay elements arising in various problems involving delay compensation or preview utilization. Several approaches to reduce implementation complexity, understood as the number of delays required to attain a required accuracy level, are put forward. First, we derive the H2-optimal coefficients for a given delay pattern. This can be seen as a problem-oriented alternative to traditionally used Newton-Cotes numerical integration rules. Second, we propose a computationally efficient method for finding the H2-optimal delay pattern, which uses dynamic programming on multistage graphs. Third, we propose a convex optimization approach, based on ℓ1 heuristics, of reducing the number of delays under hard bounds on the H∞-norm of the approximation error. Numerical simulations demonstrate efficiency of the proposed algorithms. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Numerical methods, Time-delay systems, Dead-time compensation
host publication
[Host publication title missing]
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
52nd IEEE Conference on Decision and Control, 2013
conference location
Florence, Italy
conference dates
2013-12-10 - 2013-12-13
external identifiers
  • scopus:84902354705
language
English
LU publication?
yes
id
f8dc14c0-e2df-435a-9ee7-0c1b10b31c58 (old id 5045775)
date added to LUP
2016-04-04 10:21:17
date last changed
2022-01-29 20:09:56
@inproceedings{f8dc14c0-e2df-435a-9ee7-0c1b10b31c58,
  abstract     = {{This note studies lumped-delay approximations of distributed-delay elements arising in various problems involving delay compensation or preview utilization. Several approaches to reduce implementation complexity, understood as the number of delays required to attain a required accuracy level, are put forward. First, we derive the H2-optimal coefficients for a given delay pattern. This can be seen as a problem-oriented alternative to traditionally used Newton-Cotes numerical integration rules. Second, we propose a computationally efficient method for finding the H2-optimal delay pattern, which uses dynamic programming on multistage graphs. Third, we propose a convex optimization approach, based on ℓ1 heuristics, of reducing the number of delays under hard bounds on the H∞-norm of the approximation error. Numerical simulations demonstrate efficiency of the proposed algorithms.}},
  author       = {{Troeng, Olof and Mirkin, Leonid}},
  booktitle    = {{[Host publication title missing]}},
  keywords     = {{Numerical methods; Time-delay systems; Dead-time compensation}},
  language     = {{eng}},
  pages        = {{294--299}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Toward a More Efficient Implementation of Distributed-Delay Elements}},
  url          = {{https://lup.lub.lu.se/search/files/5519120/5045788.pdf}},
  year         = {{2013}},
}