On Event-Based Sampling for LQG-Optimal Control
(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:
https://lup.lub.lu.se/record/f9ead884-95f8-4fee-a323-cee1c97a7c5a
- author
- Thelander Andrén, Marcus LU ; Bernhardsson, Bo LU ; Cervin, Anton LU and Soltesz, Kristian LU
- organization
- publishing date
- 2018
- type
- Contribution to conference
- publication status
- published
- subject
- conference name
- Reglermöte 2018
- conference location
- Stockholm, Sweden
- conference dates
- 2018-06-18 - 2018-06-20
- project
- Event-Based Estimation and Control
- Event-Based Control of Stochastic Systems with Application to Server Systems
- language
- English
- LU publication?
- yes
- id
- f9ead884-95f8-4fee-a323-cee1c97a7c5a
- date added to LUP
- 2018-06-27 15:02:28
- date last changed
- 2023-12-01 13:44:09
@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}}, title = {{On Event-Based Sampling for LQG-Optimal Control}}, url = {{https://lup.lub.lu.se/search/files/46934618/poster_marcus.pdf}}, year = {{2018}}, }