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On LQG-Optimal Event-Based Sampling

Thelander Andrén, Marcus LU (2020) In Lunds tekniska högskola. Institutionen för reglerteknik
Abstract
Event-based control is a promising concept for the design of resource-efficient feedback systems, where events such as sampling, actuation, and data transmissions are triggered reactively based on monitored control performance rather than a periodic timer. In this thesis, we investigate how sampling and communication events should be triggered to fully exploit the potential of event-based control based on the classic linear–quadratic–Gaussian (LQG) framework.

The design of the event trigger is formulated as a trade-off between a quadratic cost on control performance and the average event rate. The optimal event trigger is well-known for first-order systems, where it corresponds to a scalar symmetric threshold on the monitored... (More)
Event-based control is a promising concept for the design of resource-efficient feedback systems, where events such as sampling, actuation, and data transmissions are triggered reactively based on monitored control performance rather than a periodic timer. In this thesis, we investigate how sampling and communication events should be triggered to fully exploit the potential of event-based control based on the classic linear–quadratic–Gaussian (LQG) framework.

The design of the event trigger is formulated as a trade-off between a quadratic cost on control performance and the average event rate. The optimal event trigger is well-known for first-order systems, where it corresponds to a scalar symmetric threshold on the monitored control performance. In this thesis, we consider systems of higher order, where the shape of the optimal threshold is generally unknown. For two new system classes with previously unknown solutions, we prove that the optimal threshold is ellipsoidal for all system orders. Additionally, we propose two numerical methods for finding the optimal threshold shape for general systems.

Suboptimal but simpler designs in the form of event-based proportional–integral–derivative (PID) control are also considered. Inspired by results from LQG-optimal sampled-data control, we derive an “ideal” (in the LQG sense) sampled-data PID implementation, from which a range of design options of varying complexity for event-based PID control is proposed. Based on numerical evaluations, we present a proposal implementation that strikes a balance between performance and simplicity. Finally, this thesis also considers stochastic triggering, where events are triggered according to a certain probability. Two policies for stochastic triggering are proposed for a remote state estimation problem, both featuring predictions in the sensor for improved estimation performance. Both policies compare well to other proposals from the literature, and one of the policies also offers significantly simpler performance analysis. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Assistant Professor Antunes, Duarte, Eindhoven University of Technology, Eindhoven, Nederländerna
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Event-based control, LQG control, sampled-data control, Stochastic control, Event-based PID control, Event-based state estimation, stochastic triggering
in
Lunds tekniska högskola. Institutionen för reglerteknik
pages
170 pages
publisher
Lund University
defense location
Lecture hall F, building KC4, Naturvetarvägen 18, Lund University, Faculty of Engineering LTH, Lund Join via Zoom: https://lu-se.zoom.us/j/69005529722
defense date
2020-12-17 10:15:00
ISSN
0280–5316
ISBN
978-91-7895-656-2
978-91-7895-657-9
project
Event-Based Control of Stochastic Systems with Application to Server Systems
Event-Based Estimation and Control
language
English
LU publication?
yes
id
8f3af775-387f-48ea-8b88-f9a9fb56c582
date added to LUP
2020-11-18 14:42:42
date last changed
2020-12-04 08:06:23
@phdthesis{8f3af775-387f-48ea-8b88-f9a9fb56c582,
  abstract     = {Event-based control is a promising concept for the design of resource-efficient feedback systems, where events such as sampling, actuation, and data transmissions are triggered reactively based on monitored control performance rather than a periodic timer. In this thesis, we investigate how sampling and communication events should be triggered to fully exploit the potential of event-based control based on the classic linear–quadratic–Gaussian (LQG) framework.<br/><br/>The design of the event trigger is formulated as a trade-off between a quadratic cost on control performance and the average event rate. The optimal event trigger is well-known for first-order systems, where it corresponds to a scalar symmetric threshold on the monitored control performance. In this thesis, we consider systems of higher order, where the shape of the optimal threshold is generally unknown. For two new system classes with previously unknown solutions, we prove that the optimal threshold is ellipsoidal for all system orders. Additionally, we propose two numerical methods for finding the optimal threshold shape for general systems.<br/><br/>Suboptimal but simpler designs in the form of event-based proportional–integral–derivative (PID) control are also considered. Inspired by results from LQG-optimal sampled-data control, we derive an “ideal” (in the LQG sense) sampled-data PID implementation, from which a range of design options of varying complexity for event-based PID control is proposed. Based on numerical evaluations, we present a proposal implementation that strikes a balance between performance and simplicity. Finally, this thesis also considers stochastic triggering, where events are triggered according to a certain probability. Two policies for stochastic triggering are proposed for a remote state estimation problem, both featuring predictions in the sensor for improved estimation performance. Both policies compare well to other proposals from the literature, and one of the policies also offers significantly simpler performance analysis.},
  author       = {Thelander Andrén, Marcus},
  isbn         = {978-91-7895-656-2},
  issn         = {0280–5316},
  language     = {eng},
  publisher    = {Lund University},
  school       = {Lund University},
  series       = {Lunds tekniska högskola. Institutionen för reglerteknik},
  title        = {On LQG-Optimal Event-Based Sampling},
  url          = {https://lup.lub.lu.se/search/ws/files/86986914/thesis.pdf},
  year         = {2020},
}