On the minimum attention control problem for linear systems : a linear programming approach

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

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Abstract

In this paper, we present two control laws that are tailored for control applications in which computational and/or communication resources are scarce. Namely, we consider minimum attention control, where the `attention' that a control task requires is minimised given certain performance requirements, and anytime attention control, where the performance under the `attention' given by a scheduler is maximised. Here, we interpret `attention' as the inverse of the time elapsed between two consecutive executions of a control task. By focussing on linear plants, by allowing for only a finite number of possible intervals between two subsequent executions of the control task, by making a novel extension to the notion of control Lyapunov functions and taking these novel extended control Lyapunov function to be infinity-norm-based, we can formulate the aforementioned control problems as online linear programs, which can be solved efficiently. Furthermore, we provide techniques to construct suitable infinity-norm-based extended control Lyapunov functions for our purposes. Finally, we illustrate the resulting control laws using numerical examples. In particular, we show that minimum attention control outperforms an alternative implementation-aware control law available in the literature.
Original languageEnglish
Title of host publicationProceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages4717-4722
ISBN (Print)978-1-61284-800-6
DOIs
Publication statusPublished - 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Hilton Orlando Bonnet Creek, Orlando, FL, United States
Duration: 12 Dec 201115 Dec 2011
Conference number: 50
http://www.ieeecss.org/CAB/conferences/cdcecc2011/

Conference

Conference2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Abbreviated titleCDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1115/12/11
Internet address

Fingerprint

Linear programming
Linear systems
Lyapunov functions

Cite this

Donkers, M. C. F., Tabuada, P., & Heemels, W. P. M. H. (2011). On the minimum attention control problem for linear systems : a linear programming approach. In Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA (pp. 4717-4722). Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2011.6161239
Donkers, M.C.F. ; Tabuada, P. ; Heemels, W.P.M.H. / On the minimum attention control problem for linear systems : a linear programming approach. Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA. Piscataway : Institute of Electrical and Electronics Engineers, 2011. pp. 4717-4722
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Donkers, MCF, Tabuada, P & Heemels, WPMH 2011, On the minimum attention control problem for linear systems : a linear programming approach. in Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA. Institute of Electrical and Electronics Engineers, Piscataway, pp. 4717-4722, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161239

On the minimum attention control problem for linear systems : a linear programming approach. / Donkers, M.C.F.; Tabuada, P.; Heemels, W.P.M.H.

Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA. Piscataway : Institute of Electrical and Electronics Engineers, 2011. p. 4717-4722.

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

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AB - In this paper, we present two control laws that are tailored for control applications in which computational and/or communication resources are scarce. Namely, we consider minimum attention control, where the `attention' that a control task requires is minimised given certain performance requirements, and anytime attention control, where the performance under the `attention' given by a scheduler is maximised. Here, we interpret `attention' as the inverse of the time elapsed between two consecutive executions of a control task. By focussing on linear plants, by allowing for only a finite number of possible intervals between two subsequent executions of the control task, by making a novel extension to the notion of control Lyapunov functions and taking these novel extended control Lyapunov function to be infinity-norm-based, we can formulate the aforementioned control problems as online linear programs, which can be solved efficiently. Furthermore, we provide techniques to construct suitable infinity-norm-based extended control Lyapunov functions for our purposes. Finally, we illustrate the resulting control laws using numerical examples. In particular, we show that minimum attention control outperforms an alternative implementation-aware control law available in the literature.

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Donkers MCF, Tabuada P, Heemels WPMH. On the minimum attention control problem for linear systems : a linear programming approach. In Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), 12-15 December 2011, Orlando, USA. Piscataway: Institute of Electrical and Electronics Engineers. 2011. p. 4717-4722 https://doi.org/10.1109/CDC.2011.6161239