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Stochastic Event-Based Control and Estimation

Henningsson, Toivo LU (2012) In PhD Theses TFRT-1095.
Abstract
Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed.



Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner.



This thesis investigates an event-based variation on the stochastic... (More)
Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed.



Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner.



This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium.



Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming.



The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Hespanha, Joao Pedro, University of California, Santa Barbara, USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
event-based control, event-based estimation, sporadic control, stochastic control, stochastic hybrid systems, sum-of-squares methods, control over networks, quantized measurements
in
PhD Theses
volume
TFRT-1095
pages
183 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
defense location
Lecture hall M:B, M-building, Ole Römers väg 1, Lund University Faculty of Engineering
defense date
2012-12-18 10:15
ISSN
0280-5316
ISBN
978-91-7473-410-2
language
English
LU publication?
yes
id
de922e8b-9504-4dda-baff-94bdf6b53237 (old id 3166619)
date added to LUP
2012-11-22 16:05:51
date last changed
2016-09-19 08:44:48
@phdthesis{de922e8b-9504-4dda-baff-94bdf6b53237,
  abstract     = {Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed.<br/><br>
<br/><br>
Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner.<br/><br>
<br/><br>
This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium.<br/><br>
<br/><br>
Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming.<br/><br>
<br/><br>
The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error.},
  author       = {Henningsson, Toivo},
  isbn         = {978-91-7473-410-2},
  issn         = {0280-5316},
  keyword      = {event-based control,event-based estimation,sporadic control,stochastic control,stochastic hybrid systems,sum-of-squares methods,control over networks,quantized measurements},
  language     = {eng},
  pages        = {183},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  school       = {Lund University},
  series       = {PhD Theses},
  title        = {Stochastic Event-Based Control and Estimation},
  volume       = {TFRT-1095},
  year         = {2012},
}