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On Event-Based Sampling for LQG-Optimal Control

Thelander Andrén, Marcus LU ; Bernhardsson, Bo LU ; Cervin, Anton LU and Soltesz, Kristian LU (2018) 56th IEEE Annual Conference on Decision and Control, CDC 2017 In 56th IEEE Conference on Decision and Control, CDC, 2017 p.5438-5444
Abstract
We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between average sampling rate and control performance in a linear-quadratic-Gaussian (LQG) control problem setting with output feedback. Our analysis is based on a recently presented sampled-data controller structure, which remains LQG-optimal for any choice of sampling scheme. We show that optimization of the sampling scheme is related to an elliptic convection–diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A numerical method is presented to solve this problem for second order systems, and thus obtain an optimal sampling scheme. The method also directly generalizes to higher order... (More)
We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between average sampling rate and control performance in a linear-quadratic-Gaussian (LQG) control problem setting with output feedback. Our analysis is based on a recently presented sampled-data controller structure, which remains LQG-optimal for any choice of sampling scheme. We show that optimization of the sampling scheme is related to an elliptic convection–diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A numerical method is presented to solve this problem for second order systems, and thus obtain an optimal sampling scheme. The method also directly generalizes to higher order systems, although with a higher computational cost. For the special case of multidimensional integrator systems, we present the optimal sampling scheme on closed form, and prove that it will always outperform its periodic counterpart. Tight bounds on the improvement are presented. The improved performance is also demonstrated in numerical examples, both for an integrator system and a more general case.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
event-based sampling, LQG-optimal control, sampled-data control, linear reset systems
in
56th IEEE Conference on Decision and Control, CDC, 2017
pages
7 pages
conference name
56th IEEE Annual Conference on Decision and Control, CDC 2017
external identifiers
  • scopus:85046124406
DOI
10.1109/CDC.2017.8264464
language
English
LU publication?
yes
id
e701d9f6-fa8e-4733-9af8-aa320a7e476a
date added to LUP
2017-03-30 11:29:10
date last changed
2018-06-28 08:08:03
@inproceedings{e701d9f6-fa8e-4733-9af8-aa320a7e476a,
  abstract     = {We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between average sampling rate and control performance in a linear-quadratic-Gaussian (LQG) control problem setting with output feedback. Our analysis is based on a recently presented sampled-data controller structure, which remains LQG-optimal for any choice of sampling scheme. We show that optimization of the sampling scheme is related to an elliptic convection–diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A numerical method is presented to solve this problem for second order systems, and thus obtain an optimal sampling scheme. The method also directly generalizes to higher order systems, although with a higher computational cost. For the special case of multidimensional integrator systems, we present the optimal sampling scheme on closed form, and prove that it will always outperform its periodic counterpart. Tight bounds on the improvement are presented. The improved performance is also demonstrated in numerical examples, both for an integrator system and a more general case.<br/>},
  author       = {Thelander Andrén, Marcus and Bernhardsson, Bo and Cervin, Anton and Soltesz, Kristian},
  booktitle    = {56th IEEE Conference on Decision and Control, CDC, 2017},
  keyword      = {event-based sampling,LQG-optimal control,sampled-data control,linear reset systems},
  language     = {eng},
  pages        = {5438--5444},
  title        = {On Event-Based Sampling for LQG-Optimal Control},
  url          = {http://dx.doi.org/10.1109/CDC.2017.8264464},
  year         = {2018},
}