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The Optimal Sampling Pattern for Linear Control Systems

Bini, Enrico LU and Buttazzo, Giuseppe (2014) In IEEE Transactions on Automatic Control 59(1). p.78-90
Abstract
In digital control systems, the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. With the optimal sampling problem, we mean the selection of sampling instants and control inputs, such that a given function of the state and input is minimized. In this paper, we formulate the optimal sampling problem and we derive a necessary condition of the LQR optimality of a set of sampling instants. Since the numerical solution of the optimal sampling problem is very time consuming, we also propose a new quantization-based sampling strategy that is computationally tractable and capable of achieving near-optimal cost. Finally, and probably most interesting of all, we prove that the... (More)
In digital control systems, the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. With the optimal sampling problem, we mean the selection of sampling instants and control inputs, such that a given function of the state and input is minimized. In this paper, we formulate the optimal sampling problem and we derive a necessary condition of the LQR optimality of a set of sampling instants. Since the numerical solution of the optimal sampling problem is very time consuming, we also propose a new quantization-based sampling strategy that is computationally tractable and capable of achieving near-optimal cost. Finally, and probably most interesting of all, we prove that the quantization-based sampling is optimal in first-order systems for a large number of samples. Experiments demonstrate that quantization-based sampling has near-optimal performance even when

the system has a higher order. However, it is still an open question whether quantization-based sampling is asymptotically optimal in

any case. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Automatic Control
volume
59
issue
1
pages
78 - 90
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • WOS:000330760400006
  • Scopus:84891620553
ISSN
0018-9286
DOI
10.1109/TAC.2013.2279913
language
English
LU publication?
yes
id
57c49730-0852-4d48-947d-fe56708a7070 (old id 4178539)
date added to LUP
2013-12-02 09:50:39
date last changed
2016-10-13 04:28:00
@misc{57c49730-0852-4d48-947d-fe56708a7070,
  abstract     = {In digital control systems, the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. With the optimal sampling problem, we mean the selection of sampling instants and control inputs, such that a given function of the state and input is minimized. In this paper, we formulate the optimal sampling problem and we derive a necessary condition of the LQR optimality of a set of sampling instants. Since the numerical solution of the optimal sampling problem is very time consuming, we also propose a new quantization-based sampling strategy that is computationally tractable and capable of achieving near-optimal cost. Finally, and probably most interesting of all, we prove that the quantization-based sampling is optimal in first-order systems for a large number of samples. Experiments demonstrate that quantization-based sampling has near-optimal performance even when<br/><br>
the system has a higher order. However, it is still an open question whether quantization-based sampling is asymptotically optimal in<br/><br>
any case.},
  author       = {Bini, Enrico and Buttazzo, Giuseppe},
  issn         = {0018-9286},
  language     = {eng},
  number       = {1},
  pages        = {78--90},
  publisher    = {ARRAY(0xabf3258)},
  series       = {IEEE Transactions on Automatic Control},
  title        = {The Optimal Sampling Pattern for Linear Control Systems},
  url          = {http://dx.doi.org/10.1109/TAC.2013.2279913},
  volume       = {59},
  year         = {2014},
}