Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference 2009
DOI: 10.1109/cdc.2009.5400541
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On Lyapunov sampling for event-driven controllers

Abstract: Abstract-This paper investigates an event condition for event-driven controllers based on Lyapunov functions. Considering that constant values of a Lyapunov function define contour curves that form closed regions around the equilibrium point, in this paper we present a sampling mechanism that enforces job executions (sampling, control algorithm computation and actuation) each time the system trajectory reaches a given contour curve. By construction, the sequence of generated samples is stable in the discrete L… Show more

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Cited by 69 publications
(76 citation statements)
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“…Some stability and robustness proprieties are exploited inÅström and Bernhardsson (2002); Heemels et al (2009);Lunze and Lehmann (2010); Donkers and Heemels (2010); Eqtami et al (2010). An alternative approach consists in taking events related to the variation of a Lyapunov function -and consequently to the state too -between the current state and its value at the last sampling, like in Velasco et al (2009), or in taking events related to the time derivative of the Lyapunov function, like in Tabuada (2007); Anta and Tabuada (2008); Marchand et al (2011Marchand et al ( , 2013. More particularly, the work in Marchand et al (2013) is based on the universal formula of Sontag (1989).…”
Section: Introductionmentioning
confidence: 99%
“…Some stability and robustness proprieties are exploited inÅström and Bernhardsson (2002); Heemels et al (2009);Lunze and Lehmann (2010); Donkers and Heemels (2010); Eqtami et al (2010). An alternative approach consists in taking events related to the variation of a Lyapunov function -and consequently to the state too -between the current state and its value at the last sampling, like in Velasco et al (2009), or in taking events related to the time derivative of the Lyapunov function, like in Tabuada (2007); Anta and Tabuada (2008); Marchand et al (2011Marchand et al ( , 2013. More particularly, the work in Marchand et al (2013) is based on the universal formula of Sontag (1989).…”
Section: Introductionmentioning
confidence: 99%
“…Each networked control loop triggers its control updates when its own event condition of the form (4) (with inequality), defined in terms of its particular Lyapunov function, holds. This would be the direct but unrealistic application of the Lyapunov sampling approach [9] to NCS, unrealistic in the sense that no bus contention problems are considered. Although it is not realistic, it provides interesting numbers for baseline comparisons.…”
Section: Simulation Set-upmentioning
confidence: 99%
“…It is well accepted that event-driven sampling methods offer controllers with a lower resource utilization than standard periodic discrete-time control laws. Recent and representative results on event-driven control can be found in [2], [3], [6], [12] and [9].…”
Section: Introductionmentioning
confidence: 99%
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