Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication

W.P.M.H. Heemels, D.P. Borgers, V.S. Dolk, R. Geiselhart, S.H.J. Heijmans

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

In this tutorial presentation we focus on the construction of Lyapunov or storage functions for large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. Within each packet-based communication network only one node can communicate at a given transmission time (requiring communication protocols) and the transmission intervals and delays may vary over time. These artefacts cause network-induced communication errors in the overal closed-loop system and can be detrimental for stability and performance. For these NCSs we provide explicit constructions of Lyapunov functions by modelling the large-scale NCS as an interconnection of a finite or even an infinite number of hybrid subsystems, and combining 'local' Lyapunov functions for the controlled dynamics (including network-induced errors) and the protocols in a systematic manner. These constructions lead to the numerical computation of maximum allowable transmission intervals (MATIs) and maximum allowable delays (MADs) for each of the individual networks. The availability of the Lyapunov or storage functions guarantee properties such as global asymptotic or exponential stability, input-to-state stability (ISS) and Lp-stability for the large-scale NCS. Interestingly, the control performance expressed in terms of ISS and Lp-gains can be traded with the network parameters (MATIs and MADs). Hence, tradeoffs can be made between the quality-of-control of the overal hybrid system and the required quality-of-service of the underlying communication infrastructure. Also event-triggered communication schemes will be shortly discussed. The results are illustrated with an example of vehicle platooning.

Original languageEnglish
Title of host publication2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages936-938
Number of pages3
ISBN (Electronic)978-1-5090-2591-6
ISBN (Print)978-1-5090-2592-3
DOIs
Publication statusPublished - 6 Jan 2017
Event15th European Control Conference (ECC 2016) - Aalborg, Denmark
Duration: 29 Jun 20161 Jul 2016
Conference number: 15
http://www.ecc16.eu/index.shtml
http://www.ecc16.eu/index.shtml

Conference

Conference15th European Control Conference (ECC 2016)
Abbreviated titleECC 2016
CountryDenmark
CityAalborg
Period29/06/161/07/16
Internet address

Fingerprint

Networked control systems
Networked Control Systems
Lyapunov functions
Lyapunov Function
Communication
Asymptotic stability
Communication Networks
Lyapunov
Telecommunication networks
Interval
Network protocols
Global Exponential Stability
Dynamic Networks
Global Asymptotic Stability
Communication Protocol
Hybrid systems
Hybrid Systems
Closed loop systems
Interconnection
Numerical Computation

Cite this

Heemels, W. P. M. H., Borgers, D. P., Dolk, V. S., Geiselhart, R., & Heijmans, S. H. J. (2017). Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication. In 2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark (pp. 936-938). [7810409] Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ECC.2016.7810409
Heemels, W.P.M.H. ; Borgers, D.P. ; Dolk, V.S. ; Geiselhart, R. ; Heijmans, S.H.J. / Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication. 2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark . Piscataway : Institute of Electrical and Electronics Engineers, 2017. pp. 936-938
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Heemels, WPMH, Borgers, DP, Dolk, VS, Geiselhart, R & Heijmans, SHJ 2017, Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication. in 2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark ., 7810409, Institute of Electrical and Electronics Engineers, Piscataway, pp. 936-938, 15th European Control Conference (ECC 2016), Aalborg, Denmark, 29/06/16. https://doi.org/10.1109/ECC.2016.7810409

Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication. / Heemels, W.P.M.H.; Borgers, D.P.; Dolk, V.S.; Geiselhart, R.; Heijmans, S.H.J.

2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark . Piscataway : Institute of Electrical and Electronics Engineers, 2017. p. 936-938 7810409.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - In this tutorial presentation we focus on the construction of Lyapunov or storage functions for large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. Within each packet-based communication network only one node can communicate at a given transmission time (requiring communication protocols) and the transmission intervals and delays may vary over time. These artefacts cause network-induced communication errors in the overal closed-loop system and can be detrimental for stability and performance. For these NCSs we provide explicit constructions of Lyapunov functions by modelling the large-scale NCS as an interconnection of a finite or even an infinite number of hybrid subsystems, and combining 'local' Lyapunov functions for the controlled dynamics (including network-induced errors) and the protocols in a systematic manner. These constructions lead to the numerical computation of maximum allowable transmission intervals (MATIs) and maximum allowable delays (MADs) for each of the individual networks. The availability of the Lyapunov or storage functions guarantee properties such as global asymptotic or exponential stability, input-to-state stability (ISS) and Lp-stability for the large-scale NCS. Interestingly, the control performance expressed in terms of ISS and Lp-gains can be traded with the network parameters (MATIs and MADs). Hence, tradeoffs can be made between the quality-of-control of the overal hybrid system and the required quality-of-service of the underlying communication infrastructure. Also event-triggered communication schemes will be shortly discussed. The results are illustrated with an example of vehicle platooning.

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Heemels WPMH, Borgers DP, Dolk VS, Geiselhart R, Heijmans SHJ. Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication. In 2016 European Control Conference (ECC), 29 June - 1 July 2016, Aalborg, Denmark . Piscataway: Institute of Electrical and Electronics Engineers. 2017. p. 936-938. 7810409 https://doi.org/10.1109/ECC.2016.7810409