Abstract

This paper presents a distributed energy-saving lighting strategy for the arrangements of a lighting network consisting of a group of light-emitting diode (LED) lamps and users. LED lamps have a dimming support feature to meet the illuminance requirements imposed by individual users. Both groups interact with each other via visible light communication (VLC) or other wireless communication features. This work aims to identify a configuration of lamps leading to the maximal energy saving in adaptive and distributed ways. To this end, a distributed assignment strategy is developed based on a message-passing framework where only local interactions among lamps and users are allowed for calculations and exchanges of the information on their status. The simulation results show that the proposed algorithm outperforms other distributed algorithms in a range of indoor lighting configurations.

© 2013 OSA

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  9. K.-I. Ahn, J. K. Kwon, “Color intensity modulation for multicolored visible light communications,” IEEE Photon. Technol. Lett. 24(24), 2254–2257 (2012).
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  10. Y. U. Lee, M. Kavehrad, “Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless network,” IEEE Trans. Consum. Electron. 58(4), 1176–1184 (2012).
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  12. J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. IEEE Standard for Local and Metropolitan Area Networks–Part 15.7: Short-Range Wireless Optical Communication Using Visible LightIEEE Standard 802.15.7-2011 (2011).
  26. Z.-Q. Luo, P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM J. Control Optim. 30(2), 408–425 (1992).
    [CrossRef]
  27. S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
    [CrossRef]
  28. CVX Research Inc., CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx (2012).

2013

Y. K. Tan, T. P. Huynh, Z. Wang, “Smart personal sensor network control for energy saving in DC grid powered LED lighting system,” IEEE Trans. on Smart Grid 4(2), 669–676, (2013).
[CrossRef]

D. Caicedo, A. Pandharipande, “Distributed illumination control with local sensing and actuation in networked lighting systems,” IEEE Sensors Journal 13(3), 1092–1104 (2013).
[CrossRef]

X.-H. Lee, I. Moreno, C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21, 10612–10621 (2013).
[CrossRef] [PubMed]

2012

J. Dong, A. Pandharipande, “Efficient distributed control of light-emitting diode array lighting systems,” Opt. Letters 37, 2910–2912 (2012).
[CrossRef]

K.-I. Ahn, J. K. Kwon, “Color intensity modulation for multicolored visible light communications,” IEEE Photon. Technol. Lett. 24(24), 2254–2257 (2012).
[CrossRef]

Y. U. Lee, M. Kavehrad, “Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless network,” IEEE Trans. Consum. Electron. 58(4), 1176–1184 (2012).
[CrossRef]

2011

S.-Y. Jung, S. Hann, C.-S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57(4), 1592–1597 (2011).
[CrossRef]

H. Elgala, R. Mesleh, H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[CrossRef]

D. Caicedo, A. Pandharipande, G. Leus, “Occupancy-based illumination control of LED lighting systems,” Lighting Res. Technol. 43, 217–234 (2011).
[CrossRef]

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

J. Dong, W. van Driel, G. Zhang, “Automatic diagnosis and control of distributed solid state lighting systems,” Opt. Express 19, 5772–5784 (2011).
[CrossRef] [PubMed]

S. Wang, K. Wang, F. Chen, S. Liu, “Design of primary optics for LED chip array in road lighting application,” Opt. Express 19, A716–A724 (2011).
[CrossRef] [PubMed]

2010

2009

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
[CrossRef]

2005

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

2004

T. Komine, M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004).
[CrossRef]

2001

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory 47(2), 498–519 (2001).
[CrossRef]

1992

Z.-Q. Luo, P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM J. Control Optim. 30(2), 408–425 (1992).
[CrossRef]

1969

M.R. Hestenes, “Multiplier and gradient methods,” J. Optim. Theory Appl. 4, 303–320 (1969).
[CrossRef]

Ahn, K.-I.

K.-I. Ahn, J. K. Kwon, “Color intensity modulation for multicolored visible light communications,” IEEE Photon. Technol. Lett. 24(24), 2254–2257 (2012).
[CrossRef]

Amamiya, A.

M. Miki, A. Amamiya, T. Hiroyasu, “Distributed optimal control of lighting based on stochastic hill climbing method with variable neighborhood,” in Proceedings of IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2007), 1676–1680.

Asratian, A. S.

A. S. Asratian, T. M. J. Denley, R. Haggkvist, Bipartite Graphs and their Applications (Cambridge University Press, 1998).
[CrossRef]

Bhardwaj, S.

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

Boyd, S.

S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
[CrossRef]

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

Caicedo, D.

D. Caicedo, A. Pandharipande, “Distributed illumination control with local sensing and actuation in networked lighting systems,” IEEE Sensors Journal 13(3), 1092–1104 (2013).
[CrossRef]

D. Caicedo, A. Pandharipande, G. Leus, “Occupancy-based illumination control of LED lighting systems,” Lighting Res. Technol. 43, 217–234 (2011).
[CrossRef]

Chen, F.

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

Colak, S. B.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

Denley, T. M. J.

A. S. Asratian, T. M. J. Denley, R. Haggkvist, Bipartite Graphs and their Applications (Cambridge University Press, 1998).
[CrossRef]

Dong, J.

J. Dong, A. Pandharipande, “Efficient distributed control of light-emitting diode array lighting systems,” Opt. Letters 37, 2910–2912 (2012).
[CrossRef]

J. Dong, W. van Driel, G. Zhang, “Automatic diagnosis and control of distributed solid state lighting systems,” Opt. Express 19, 5772–5784 (2011).
[CrossRef] [PubMed]

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

Elgala, H.

H. Elgala, R. Mesleh, H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[CrossRef]

Feng, Z.

Feri, L.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

Frey, B. J.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory 47(2), 498–519 (2001).
[CrossRef]

Garrett, J.

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

Guestrin, C.

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

Haas, H.

H. Elgala, R. Mesleh, H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[CrossRef]

Haggkvist, R.

A. S. Asratian, T. M. J. Denley, R. Haggkvist, Bipartite Graphs and their Applications (Cambridge University Press, 1998).
[CrossRef]

Han, Y.

Hann, S.

S.-Y. Jung, S. Hann, C.-S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57(4), 1592–1597 (2011).
[CrossRef]

Hestenes, M.R.

M.R. Hestenes, “Multiplier and gradient methods,” J. Optim. Theory Appl. 4, 303–320 (1969).
[CrossRef]

Hiroyasu, T.

M. Miki, A. Amamiya, T. Hiroyasu, “Distributed optimal control of lighting based on stochastic hill climbing method with variable neighborhood,” in Proceedings of IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2007), 1676–1680.

Huynh, T. P.

Y. K. Tan, T. P. Huynh, Z. Wang, “Smart personal sensor network control for energy saving in DC grid powered LED lighting system,” IEEE Trans. on Smart Grid 4(2), 669–676, (2013).
[CrossRef]

Jung, S.-Y.

S.-Y. Jung, S. Hann, C.-S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57(4), 1592–1597 (2011).
[CrossRef]

Kavehrad, M.

Y. U. Lee, M. Kavehrad, “Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless network,” IEEE Trans. Consum. Electron. 58(4), 1176–1184 (2012).
[CrossRef]

Komine, T.

T. Komine, M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004).
[CrossRef]

Krause, A.

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

Kschischang, F. R.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory 47(2), 498–519 (2001).
[CrossRef]

Kuo, C.-C.

Kwon, J. K.

K.-I. Ahn, J. K. Kwon, “Color intensity modulation for multicolored visible light communications,” IEEE Photon. Technol. Lett. 24(24), 2254–2257 (2012).
[CrossRef]

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22(19), 1455–1457 (2010).
[CrossRef]

Lee, X.-H.

Lee, Y. U.

Y. U. Lee, M. Kavehrad, “Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless network,” IEEE Trans. Consum. Electron. 58(4), 1176–1184 (2012).
[CrossRef]

Leus, G.

D. Caicedo, A. Pandharipande, G. Leus, “Occupancy-based illumination control of LED lighting systems,” Lighting Res. Technol. 43, 217–234 (2011).
[CrossRef]

Linnartz, J.-P.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

Liu, S.

Loeliger, H.-A.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory 47(2), 498–519 (2001).
[CrossRef]

Lukkien, J.

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

Luo, Y.

Luo, Z.-Q.

Z.-Q. Luo, P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM J. Control Optim. 30(2), 408–425 (1992).
[CrossRef]

Matthews, H. S.

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

Mesleh, R.

H. Elgala, R. Mesleh, H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[CrossRef]

Miki, M.

M. Miki, A. Amamiya, T. Hiroyasu, “Distributed optimal control of lighting based on stochastic hill climbing method with variable neighborhood,” in Proceedings of IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2007), 1676–1680.

Moreno, I.

Nakagawa, M.

T. Komine, M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004).
[CrossRef]

Özçelebi, T.

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

Pandharipande, A.

D. Caicedo, A. Pandharipande, “Distributed illumination control with local sensing and actuation in networked lighting systems,” IEEE Sensors Journal 13(3), 1092–1104 (2013).
[CrossRef]

J. Dong, A. Pandharipande, “Efficient distributed control of light-emitting diode array lighting systems,” Opt. Letters 37, 2910–2912 (2012).
[CrossRef]

D. Caicedo, A. Pandharipande, G. Leus, “Occupancy-based illumination control of LED lighting systems,” Lighting Res. Technol. 43, 217–234 (2011).
[CrossRef]

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

Park, C.-S.

S.-Y. Jung, S. Hann, C.-S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57(4), 1592–1597 (2011).
[CrossRef]

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

Sanghavi, S.

S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
[CrossRef]

Schenk, T.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

Shah, D.

S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
[CrossRef]

Singhvi, V.

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

Sun, C.-C.

Sun, W.-S.

Tan, Y. K.

Y. K. Tan, T. P. Huynh, Z. Wang, “Smart personal sensor network control for energy saving in DC grid powered LED lighting system,” IEEE Trans. on Smart Grid 4(2), 669–676, (2013).
[CrossRef]

Tseng, P.

Z.-Q. Luo, P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM J. Control Optim. 30(2), 408–425 (1992).
[CrossRef]

Tsuei, C.-H.

van Driel, W.

Vandenberghe, L.

S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
[CrossRef]

Verhoeven, R.

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

Wang, K.

Wang, S.

Wang, Z.

Y. K. Tan, T. P. Huynh, Z. Wang, “Smart personal sensor network control for energy saving in DC grid powered LED lighting system,” IEEE Trans. on Smart Grid 4(2), 669–676, (2013).
[CrossRef]

Willsky, A.

S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
[CrossRef]

Yang, H.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

Zhang, G.

IEEE Commun. Mag.

H. Elgala, R. Mesleh, H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[CrossRef]

IEEE Photon. Technol. Lett.

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22(19), 1455–1457 (2010).
[CrossRef]

K.-I. Ahn, J. K. Kwon, “Color intensity modulation for multicolored visible light communications,” IEEE Photon. Technol. Lett. 24(24), 2254–2257 (2012).
[CrossRef]

IEEE Sensors Journal

D. Caicedo, A. Pandharipande, “Distributed illumination control with local sensing and actuation in networked lighting systems,” IEEE Sensors Journal 13(3), 1092–1104 (2013).
[CrossRef]

IEEE Trans. Consum. Electron.

S. Bhardwaj, T. Özçelebi, R. Verhoeven, J. Lukkien, “Smart indoor solid state lighting based on a novel illumination model and implementation,” IEEE Trans. Consum. Electron. 57(4), 1612–1621, (2011).
[CrossRef]

T. Komine, M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004).
[CrossRef]

Y. U. Lee, M. Kavehrad, “Two hybrid positioning system design techniques with lighting LEDs and ad-hoc wireless network,” IEEE Trans. Consum. Electron. 58(4), 1176–1184 (2012).
[CrossRef]

S.-Y. Jung, S. Hann, C.-S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57(4), 1592–1597 (2011).
[CrossRef]

IEEE Trans. Inform. Theory

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inform. Theory 47(2), 498–519 (2001).
[CrossRef]

S. Sanghavi, D. Shah, A. Willsky, “Message-passing for maximum weight independent set,” IEEE Trans. Inform. Theory 55(11), 4822–4834 (2009).
[CrossRef]

IEEE Trans. on Smart Grid

Y. K. Tan, T. P. Huynh, Z. Wang, “Smart personal sensor network control for energy saving in DC grid powered LED lighting system,” IEEE Trans. on Smart Grid 4(2), 669–676, (2013).
[CrossRef]

IEEE Trans. Signal Proc.

J.-P. Linnartz, L. Feri, H. Yang, S. B. Colak, T. Schenk, “Code division-based sensing of illumination contributions in solid-state lighting systems,” IEEE Trans. Signal Proc. 57(10), 3984–3998 (2009).
[CrossRef]

J. Optim. Theory Appl.

M.R. Hestenes, “Multiplier and gradient methods,” J. Optim. Theory Appl. 4, 303–320 (1969).
[CrossRef]

Lighting Res. Technol.

D. Caicedo, A. Pandharipande, G. Leus, “Occupancy-based illumination control of LED lighting systems,” Lighting Res. Technol. 43, 217–234 (2011).
[CrossRef]

Opt. Express

Opt. Letters

J. Dong, A. Pandharipande, “Efficient distributed control of light-emitting diode array lighting systems,” Opt. Letters 37, 2910–2912 (2012).
[CrossRef]

Proceedings of ACM Conference on Embedded Networked Sensor Systems

V. Singhvi, A. Krause, C. Guestrin, J. Garrett, H. S. Matthews, “Intelligent light control using sensor networks,” in Proceedings of ACM Conference on Embedded Networked Sensor Systems(2005).

SIAM J. Control Optim.

Z.-Q. Luo, P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM J. Control Optim. 30(2), 408–425 (1992).
[CrossRef]

Other

CVX Research Inc., CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx (2012).

IEEE Standard for Local and Metropolitan Area Networks–Part 15.7: Short-Range Wireless Optical Communication Using Visible LightIEEE Standard 802.15.7-2011 (2011).

A. S. Asratian, T. M. J. Denley, R. Haggkvist, Bipartite Graphs and their Applications (Cambridge University Press, 1998).
[CrossRef]

S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
[CrossRef]

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” in Foundations and Trends in Machine Learning (Now Publishers, 2011), 1–122.

M. Miki, A. Amamiya, T. Hiroyasu, “Distributed optimal control of lighting based on stochastic hill climbing method with variable neighborhood,” in Proceedings of IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2007), 1676–1680.

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Figures (12)

Fig. 1
Fig. 1

Example of an LED lighting network and associated bipartite graph.

Fig. 2
Fig. 2

LED lamps’ relative intensity levels for 15 users and 25 lamps.

Fig. 3
Fig. 3

Users’ observed illuminance levels for 15 users and 25 lamps.

Fig. 4
Fig. 4

Optimal configuration at the 950th time unit.

Fig. 5
Fig. 5

Optimal configuration at the 1950th time unit.

Fig. 6
Fig. 6

Optimal configuration at the 2950th time unit.

Fig. 7
Fig. 7

Optimal configuration at the 3950th time unit.

Fig. 8
Fig. 8

Optimal configuration at the 4950th time unit.

Fig. 9
Fig. 9

Objective values for the minimum required illuminance of 200lx.

Fig. 10
Fig. 10

Normalized errors from the optimal solution for the minimum required illuminance of 200lx.

Fig. 11
Fig. 11

Objective values for the minimum required illuminance of 400lx.

Fig. 12
Fig. 12

Normalized errors from the optimal solution for the minimum required illuminance of 400lx.

Tables (1)

Tables Icon

Algorithm 1 Distributed assignment

Equations (11)

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min x i [ 0 , 1 ] i P i x i subject to i 𝒩 ( a ) I a i x i a , a ,
min x i [ 0 , 1 ] z a 0 i P i x i subject to i 𝒩 ( a ) I a i x i z a = a , a .
max u a 0 g ( u ) min x i [ 0 , 1 ] z a 0 L ρ ( u , x , z )
L ρ ( u , x , z ) = i P i x i + ρ u T ( I x z ) + ρ 2 I x z 2 i L i ( u , x i ) + a L a ( u a , z a ) + ρ 2 I x z 2 ,
x ˜ i ( t + 1 ) = arg min x i ( P i x i + ρ 2 I i x i + I ~ i x ~ i ( t ) z ( t ) a + u ( t ) 2 ) z ˜ a ( t + 1 ) = arg min z a ( ρ 2 z a + I a x ( t + 1 ) a + u a ( t ) 2 ) u a ( t + 1 ) = u a ( t ) + ( I a x ( t + 1 ) z a ( t + 1 ) a ) x i ( t ) = 𝒯 [ 0 , 1 ] ( x ˜ i ( t ) ) z a ( t ) = 𝒯 + ( z ˜ a ( t ) ) ,
𝒯 𝒮 [ v ] = { max 𝒮 if v max 𝒮 , v if v 𝒮 , min 𝒮 if v min 𝒮 .
m a i ( t ) = a j 𝒩 ( a ) \ i I a j x j ( t ) + | z ˜ a ( t ) | ,
x i ( t + 1 ) = 𝒯 [ 0 , 1 ] [ a 𝒩 ( i ) I a i m a i ( t ) a 𝒩 ( i ) I a i 2 P i ρ a 𝒩 ( i ) I a i 2 ] ,
z ^ a ( t + 1 ) = a + i 𝒩 ( a ) I a i x i ( t + 1 ) + 𝒯 [ z ^ a ( t ) ] ,
x i ( t + 1 ) = 𝒯 [ 0 , 1 ] [ max a 𝒩 ( i ) ( λ a i ( t ) I a i P i ) ] , λ a i ( t ) = 𝒯 + [ a j 𝒩 ( a ) \ i I a j x j ( t ) ] .
x i ( t + 1 ) = 𝒯 [ 0 , 1 ] [ max χ { χ : a 𝒩 ( i ) I a i I a i χ λ a i ( t ) = P i ε } ] , λ a i ( t ) = 𝒯 + [ a j 𝒩 ( a ) \ i I a j x j ( t ) ] .

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