Abstract
We propose an event-triggered control scheme for discrete-time linear systems subject to Gaussian white noise disturbances. The event-conditions are given in terms of the deviation between the actual system state and the state of a nominal undisturbed system whose state is identical to the real system state at the event times. In order to ensure that the conditional distribution of the deviation between the two systems, under the condition that no event occurs, remains a normal distribution, we employ thresholds that are themselves random variables. This allows us to: (i) provide expressions for the probability mass function of the times between events and, in turn, arbitrarily select this function; (ii) synthesize controllers associated with the proposed transmissions scheduler that are optimal in terms of an average quadratic cost. In particular, these two properties allow us to show that our event-triggered scheme is consistent in the sense that it outperforms (in a quadratic cost sense) traditional periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances. We demonstrate the effectiveness of our scheme in a numerical example and describe a way to solve the non-convex optimization problem arising in the approach.
| Original language | English |
|---|---|
| Pages (from-to) | 376-381 |
| Number of pages | 6 |
| Journal | Automatica |
| Volume | 89 |
| DOIs | |
| Publication status | Published - 1 Mar 2018 |
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Stochastic thresholds in event-triggered control : a consistent policy for quadratic control. / Brunner, Florian David; Antunes, Duarte; Allgöwer, Frank.
In: Automatica, Vol. 89, 01.03.2018, p. 376-381.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Stochastic thresholds in event-triggered control
T2 - a consistent policy for quadratic control
AU - Brunner, Florian David
AU - Antunes, Duarte
AU - Allgöwer, Frank
PY - 2018/3/1
Y1 - 2018/3/1
N2 - We propose an event-triggered control scheme for discrete-time linear systems subject to Gaussian white noise disturbances. The event-conditions are given in terms of the deviation between the actual system state and the state of a nominal undisturbed system whose state is identical to the real system state at the event times. In order to ensure that the conditional distribution of the deviation between the two systems, under the condition that no event occurs, remains a normal distribution, we employ thresholds that are themselves random variables. This allows us to: (i) provide expressions for the probability mass function of the times between events and, in turn, arbitrarily select this function; (ii) synthesize controllers associated with the proposed transmissions scheduler that are optimal in terms of an average quadratic cost. In particular, these two properties allow us to show that our event-triggered scheme is consistent in the sense that it outperforms (in a quadratic cost sense) traditional periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances. We demonstrate the effectiveness of our scheme in a numerical example and describe a way to solve the non-convex optimization problem arising in the approach.
AB - We propose an event-triggered control scheme for discrete-time linear systems subject to Gaussian white noise disturbances. The event-conditions are given in terms of the deviation between the actual system state and the state of a nominal undisturbed system whose state is identical to the real system state at the event times. In order to ensure that the conditional distribution of the deviation between the two systems, under the condition that no event occurs, remains a normal distribution, we employ thresholds that are themselves random variables. This allows us to: (i) provide expressions for the probability mass function of the times between events and, in turn, arbitrarily select this function; (ii) synthesize controllers associated with the proposed transmissions scheduler that are optimal in terms of an average quadratic cost. In particular, these two properties allow us to show that our event-triggered scheme is consistent in the sense that it outperforms (in a quadratic cost sense) traditional periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances. We demonstrate the effectiveness of our scheme in a numerical example and describe a way to solve the non-convex optimization problem arising in the approach.
UR - http://www.scopus.com/inward/record.url?scp=85040310019&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.12.043
DO - 10.1016/j.automatica.2017.12.043
M3 - Article
AN - SCOPUS:85040310019
VL - 89
SP - 376
EP - 381
JO - Automatica
JF - Automatica
SN - 0005-1098
ER -