Advanced

On Event-Based Sampling for LQG-Optimal Control

Thelander Andrén, Marcus LU ; Bernhardsson, Bo LU ; Cervin, Anton LU and Soltesz, Kristian LU (2018) Reglermöte 2018
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to conference
publication status
published
subject
conference name
Reglermöte 2018
conference location
Stockholm, Sweden
conference dates
2018-06-18 - 2018-06-20
language
English
LU publication?
yes
id
f9ead884-95f8-4fee-a323-cee1c97a7c5a
date added to LUP
2018-06-27 15:02:28
date last changed
2019-03-28 04:00:52
@misc{f9ead884-95f8-4fee-a323-cee1c97a7c5a,
  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.},
  author       = {Thelander Andrén, Marcus and Bernhardsson, Bo and Cervin, Anton and Soltesz, Kristian},
  language     = {eng},
  location     = {Stockholm, Sweden},
  month        = {06},
  title        = {On Event-Based Sampling for LQG-Optimal Control},
  year         = {2018},
}