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1 Sensors 009, 9, ; do: /s Artcle OPEN ACCESS sensors ISSN Dstrbuted Envronment Control Usng Wreless Sensor/Actuator Networks for Lghtng Applcatons Masayuk Nakamura *, Atsush Sakura and Jro Nakamura NTT Energy and Envronment Systems Laboratores, Nppon Telegraph and Telephone Corporaton, Mornosato Wakamya, Atsug-sh, Kanagawa Pref., Japan; E-Mals: (A.S.); (J.N.) * Author to whom correspondence should be addressed; E-Mal: masayuk@aecl.ntt.co.jp; Tel.: ; Fax: Receved: 14 September 009; n revsed form: October 009 / Accepted: 3 October 009 / Publshed: 8 October 009 Abstract: We propose a decentralzed algorthm to calculate the control sgnals for lghts n wreless sensor/actuator networks. Ths algorthm uses an approprate step sze n the teratve process used for quckly computng the control sgnals. We demonstrate the accuracy and effcency of ths approach compared wth the penalty method by usng Mote-based mesh sensor networks. The estmaton error of the new approach s one-eghth as large as that of the penalty method wth one-ffth of ts computaton tme. In addton, we descrbe our sensor/actuator node for dstrbuted lghtng control based on the decentralzed algorthm and demonstrate ts practcal effcacy. Keywords: sensor/actuator network; dstrbuted control; decentralzed system 1. Introducton Wreless sensor/actuator networks (WSANs) have been nvestgated n addton to wreless sensor networks (WSNs) snce WSANs have more attractve and useful applcatons than WSNs alone. In WSNs, the man objectve s to gather raw sensor data or estmate the condton of the envronment. From such a sensng standpont, Zhao et al. proposed collaboratve sgnal and nformaton processng (CSIP) to target trackng problems [1]. They showed that collaboratve and decentralzed sensor networks are scalable and effcent as regards sensng and communcaton. Rabbat et al. nvestgated dstrbuted algorthms for sensor network data processng []. They formulated estmaton problems as optmzaton problems n dstrbuted WSNs. WSANs have the potental to expand WSN applcatons,

2 Sensors 009, enablng the nodes to perform both sensng and actuaton [3-5]. A promsng WSAN applcaton s the control of spatally dstrbuted actuators, such as dmmable lghtng ballasts, swtches and ar condtonng systems. WSANs can save energy because they can accurately montor envronmental condtons and thus control the actuators precsely. In ths context, Taylor et al. developed WSANs for energy management n heatng, ventlaton, and ar-condtonng (HVAC) systems [6]. Zhang et al. proposed a feld estmaton technque that uses WSANs to control HVAC systems n buldngs [7]. L et al. developed WSANs for lghtng control n the home envronment [8]. One challenge s to develop algorthms that save energy wthout sacrfcng user comfort. Sandhu et al. proposed WSANs for lghtng control usng a mult-agent system [9]. Snghv et al. developed a centralzed lghtng system to ncrease user comfort and reduce energy costs by usng Motes [10]. Ln et al. proposed a decentralzed algorthm for WSANs for optmal lghtng control [11]. We proposed WSANs that can provde optmal actuator control wth respect to energy savng and control sgnal qualty as well as sensng [1]. The sensor/actuator nodes perform sensng and actuaton autonomously. However, the decentralzed algorthm s based on the penalty functon method, and t takes a long tme to compute optmal control sgnals. In ths paper, we ntroduce an mproved collaboratve sensng and actuaton algorthm n an optmzaton framework for controllng lghts n workplaces. In our algorthm, an objectve functon s defned that balances energy savng aganst control sgnal qualty. We descrbe a decentralzed algorthm that s more scalable than the centralzed one, and that can autonomously calculate control sgnals wthout a central server. Ths algorthm uses an approprate step sze n the teratve process for calculatng control sgnals. We demonstrate ts accuracy and effcency compared wth the prevously proposed method by smulatons. We also carry out WSAN experments usng Motes to examne the feasblty of the algorthm. We show that the estmaton error of the proposed method s one-eghth as large as that of the prevous method wth one-ffth of ts computaton tme. In addton, we descrbe a testbed that conssts of Motes and nfrared (IR) remote controls for dstrbuted lghtng control based on the decentralzed algorthm.. Dstrbuted WSAN Model In dense dstrbuted WSANs, collaboratve processng s essental for ntellgent sensng and for controllng envronments such as shared workplaces. To conserve energy, local sensng usually determnes the local actuaton of, for example, a lght by usng an occupancy sensor. When sensor/actuator nodes are networked, the qualty of the control sgnals wthn the WSANs s mproved, resultng n occupant satsfacton. In ths paper, we use "control sgnal" as the sgnal appled to actuators. We assume that a control sgnal, for example a current, corresponds to the controlled envronmental condton, such as the brghtness of lghts. We focus on the energy savng of the lghts. In addton, the spatal smoothness of brghtness s lkely to be preferred by users. We propose a method that balances energy savng and the spatal smoothness of the control sgnals to mprove control sgnal qualty. Our method s formulated as an optmzaton problem. Let J be an objectve functon defned as:

3 Sensors 009, J 1 n α ( ( f ) (1 ) f j + α f = 1 j N = ), (1) where n s the number of sensor nodes, f s the control sgnal of sensor node, f j s the control sgnal of sensor node j wthn the communcaton range N of sensor node, and α ( 0 < α < 1) s a tradeoff parameter balancng 1 n 1 ( ( f ) f j ) n Equaton (1) (the spatal roughness of the control sgnals) aganst 1 n f = 1 = 1 j N (the consumed energy). For ths dscusson, let us consder that the sensors are passve nfrared (PIR) occupancy sensors that detect the presence of people, and that the controlled actuators are lghts. Occupancy sensor response s s bnary such that: 1 (detect) s = 0 (not detect). () The lghts are turned on n areas where people are present. To smplfy the problem, we assume that the control sgnals are set at 1 where people are present, that s: f = 1 f s = 1. (3) Mnmzng J wth respect to f means that lghts must be turned on n areas where people are present and controlled to balance the spatal smoothness of the control sgnals and energy savng otherwse. To obtan f that mnmzes J, the partal dervatve of J wth respect to f s calculated as: J / f = α ( f f j ) + (1 α) f = 0 f s = 0. (4) j N Equaton (4) s a smultaneous equaton whch represents a centralzed algorthm. It can be solved by a server collectng sensor responses from all sensor nodes. After collectng the sensor responses { s1,, s 1, s, s+ 1,, sn}, the server computes control sgnals { f1,, f 1, f, f + 1,, f n} by solvng Equaton (4) and sends the resultng control sgnals back to the sensor nodes. The sensor nodes control ther external actuators through ther dgtal output ports dependng on the control sgnals. It s also possble to use a decentralzed algorthm, whch can compute each control sgnal wthout a server. Rabbat et al. showed that dstrbuted optmzaton algorthms are more effcent than centralzed ones n terms of energy and communcatons []. The gradent method can be used to determne the value of f that mnmzes J [13]. Usng the gradent method, f s ncrementally updated by Δf as: Δf = ε J / f = ε ( α j N ( f f ) + (1 α) f ) j where ε s a postve step sze. Formerly J was redefned to nclude the condton of Equaton (3) usng the penalty functon method [1]. Ths approach was very useful for formulatng the objectve functon wthout classfyng the values of s. However, the convergence of f was very slow. In ths paper, f s computed separately by Equatons (3) and (5) dependng on the values of s. f s = 0, (5)

4 Sensors 009, Fgure 1. Decentralzed sensor/actuator network system and calculated brghtness of each node. Fgure. Two-dmensonal schematc dagram of sgnal propagaton for actvaton. Fgure 1 shows a decentralzed sensor/actuator network system n a shared workplace and an example of calculated brghtness for each node. Each sensor node s arranged at regular ntervals and communcates wth neghborng nodes to compute ts control sgnal locally. In ths model, there s no central server collectng sensor data and computng control sgnals. It s necessary to repeat the

5 Sensors 009, updates descrbed by Equaton (5) and the communcatons of the control sgnals between neghborng nodes. Fgure shows the two-dmensonal sensor node arrangement and how the sgnals propagate n the network for actvaton. To smplfy the problem, sensor nodes were arranged at regular ntervals to form a mesh network. The dashed crcle N represents the communcaton range of sensor node, whch covers neghborng nodes. Frst, the nodes detect people and become actve. Then they communcate ther sgnals to neghborng nodes. The nodes that receve the sgnals become actve n turn so that fnally all the nodes are actve. Fgure 3 shows how the control sgnals propagate after actvaton. They compute ther control sgnals and communcate them to ther neghborng nodes n turn. In ths way, the control sgnals are computed as they propagate through the network. After some communcaton and computaton teratons, each node provdes the optmal control sgnal for envronment control. Fgure 3. Two-dmensonal schematc dagram of control sgnal computaton. It s very mportant to reduce the number of teratons n ths process. We have to determne a large ε value that ensures the stablty of Equaton (5). Suppose that m sensor nodes detect the presence of people. Then Equaton (4) s represented as: Hf d = 0 f s = 0, (6) where H s an (n-m) (n-m) matrx, and f and d are n-m element column vectors. The elements of H satsfy the followng equaton: Then we have: h n m h j 1-α 0. (7) j = 1 > j h n m 1 j > h j, (8) j = and H s strctly dagonally domnant and regular [14].

6 Sensors 009, In addton, because the dagonal elements of H are postve: h > 0 (9) H s a postve defnte matrx. To guarantee the stablty of Equaton (5), we have the followng equaton [1]: 0 max < ε < / λ, (10) where λ max s the largest egenvalue of H. Wth the penalty functon method, there are large values n the dagonal elements and large egenvalues of H because the penalty parameter s usually large (e.g. 100) [1]. Therefore, we had to use a small ε value, whch resulted n the slow computaton of f. In contrast, we can apply a larger ε to Equaton (5) than wth the penalty functon method snce we have a smaller λ max than that of the penalty functon method. Ths s expected to lead to the fast and precse computaton of the control sgnals. 3. Expermental Crossbow Motes, MICADOTs equpped wth PIR occupancy sensors (AMN 1311, Matsushta Electrc Works, Ltd.) were used as the sensor/actuator network testbed. A MICADOT conssts of an Atmega18 mcrocontroller (4 MHz) and a CC1000 rado (315 MHz). The occupancy sensor can be easly attached to the 10-bt A/D converter of the Mote. The sensor readng ranged from 0 to 103. The software was TnyOS1.1 [15]. Fgure 4. Dstrbuted actuaton experment usng Motes. Frst, we examned the decentralzed algorthm by smulatons and by mplementng t usng Motes. A Mote has dgtal I/O pns that can control electronc components such as lghts. In ths experment, Motes were assumed to detect occupancy by usng the PIR sensors and control lghts. We assumed that the sensor/actuator nodes were arranged on the celng n a shared workplace. The lghts are controlled dependng on the response of the occupancy sensors. Bascally, the occuped areas must be brght and the unoccuped areas may be dark. Any nonunformty of brghtness may be unacceptable to the occupants. Therefore, both energy savng and smoothness of spatal brghtness must be taken nto

7 Sensors 009, consderaton. In ths experment, we used 5 Motes, each wth an occupancy sensor. Each node s samplng tme was s and ts neghborng nodes were fxed regardless of the wreless communcaton range. All nodes were assumed to have a lght control unt wth a dgtal output port. Fgure 4 shows the expermental setup. Nodes 1, 4 and 19 detected the presence of people and communcated ther sgnals to the neghborng nodes. Frst we nvestgated the resultng control sgnals usng the penalty functon method. There were 50 communcaton teratons. Then we evaluated the proposed decentralzed algorthm. There were 10 communcaton teratons. Next, we developed a testbed for WSANs based on Motes. The sensor/actuator node conssts of a MICADOT, a PIC mcrocontroller (PIC1F69, Mcrochp Technology Inc.), a PIR occupancy sensor and an IR LED for remote control. The IR LED s drven by the PIC mcrocontroller and generates remote control sgnals for lghts. The lght has an IR detector for readng the control sgnals. Lghtng brghtness can vary by eght magntudes dependng on the control sgnals from the Mote. In ths experment, three lghts were deployed on the celng and three correspondng nodes were placed on the desk (Fgure 5). Each node detected occupancy and communcated the control sgnal to ts neghborng nodes, and then controlled the brghtness of a unque lght rght above t. The Mote s wreless communcaton range was lmted to approxmately m. Fgure 6 s a photograph of a dstrbuted lghtng experment. Frst, the three nodes detected three people and set the correspondng lghts at maxmum brghtness. When the two people at nodes 1 and 3 left ther desks, the nodes detected the occupancy changes {s 1,s,s 3 } = {0,1,0} and began to compute the optmal brghtness by communcatng wth each other. In ths experment, the node s communcaton nterval was 5 s and the nodes adjusted the lghts every nterval. There were 10 communcaton and control teratons, whch means a communcaton and control duraton of 50 s. Experments were also conducted for the followng occupancy changes, {s 1,s,s 3 } = {1,0,0}, {s 1,s,s 3 } = {1,0,1}, {s 1,s,s 3 } = {1,1,0}. Fgure 5. Dstrbuted lghtng control experment usng Mote testbed.

8 Sensors 009, Fgure 6. Photograph of the dstrbuted lghtng experment. 4. Results Fgure 7 compares the control sgnals smulated by the decentralzed and centralzed algorthms. Equaton (1) was redefned by the penalty functon method takng account of Equaton (3) [1]. Parameter α n Equaton (1) was 0.3. The centralzed algorthm provdes an exact soluton for modfed Equaton (4) by the penalty functon method. Ths result shows that llumnaton was provded n unpopulated areas close to an area where people were present. In the decentralzed algorthm, the ntal values of the calculated control sgnals were determned by sensor responses, that s, 1 for nodes 1, 4 and 19, and 0 for the others. The parameter ε n Equaton (6) was The root mean square (RMS) error between the centralzed and decentralzed results was Ths result ndcates that there were some errors n the estmated control sgnals when usng the decentralzed algorthm even wth a large teraton number. We must ncrease the teraton number further to obtan a better estmaton. Fgure 8 compares the expermental results for dstrbuted actuaton usng Motes mplemented wth a decentralzed algorthm and a smulaton of the centralzed algorthm. The parameters were the same as those used n Fgure 7. The Motes were mplemented wth the same decentralzed algorthm as n Fgure 7. The RMS error was It s clear that, despte some errors, Motes can provde a good estmaton. The average communcaton error rate among the Motes was 9.9%. We beleve that communcaton error led to the Motes calculaton error. When there s no communcaton error, the Motes can compute perfectly, and provde the same result as that n Fgure 7. Fgure 9 compares the control sgnals smulated by the proposed decentralzed and centralzed algorthms. The parameter ε n Equaton (6) was 0.5 and the teraton number was 10. We were able to use a larger ε and a smaller teraton number than n Fgure 7. The RMS error was , whch ndcates that ths algorthm could acheve better performance than seen n Fgure 7. Ths proposed algorthm enables WSANs to calculate the optmal control sgnals rapdly and precsely.

9 Sensors 009, Fgure 7. Expermental results of dstrbuted actuaton usng smulatons of centralzed and decentralzed algorthms. The decentralzed algorthm s based on the penalty functon method. Fgure 8. Expermental results of dstrbuted actuaton usng Motes mplemented wth decentralzed algorthm and smulaton of centralzed algorthm. The decentralzed algorthm s based on the penalty functon method.

10 Sensors 009, Fgure 9. Expermental dstrbuted actuaton results obtaned usng smulatons of centralzed and proposed decentralzed algorthms. Fgure 10. Expermental dstrbuted actuaton results obtaned usng Motes mplemented wth proposed decentralzed algorthm and smulaton of centralzed algorthm.

11 Sensors 009, Fgure 11. Smulaton result of packet loss rate vs. RMS error between centralzed and decentralzed algorthms (crcle: proposed algorthm, square: prevously proposed algorthm). Fgure 1. Occupancy pattern and expermental dstrbuted actuaton results obtaned usng Motes mplemented wth proposed decentralzed algorthm and smulaton of centralzed algorthm.

12 Sensors 009, Fgure 10 compares the calculaton results obtaned for the Motes and the centralzed algorthm by smulaton. The parameters were the same as n Fgure 9. The Motes were mplemented wth the proposed decentralzed algorthm. The RMS error was and the average communcaton error rate among the Motes was 9.7%. Compared wth Fgure 8, the RMS error of the proposed algorthm was one-eghth as large as that of the penalty method wth one-ffth of ts computaton tme. The computaton errors were caused by the communcaton errors. Ths result shows that the Motes could provde almost the same result as the smulaton n Fgure 9. It was found that the algorthm was capable of constructng practcal envronment control systems usng Motes despte the communcaton errors. Fgure 11 compares the smulaton results ndcatng that how the RMS error depends on the communcaton error for the proposed and the prevously proposed algorthms. The parameters were the same as those n Fgures 7 and 9. The Mote's average packet loss rate was approxmately 10%. The smulaton results ndcate that the proposed algorthm s robust aganst the communcaton error. In order to show that the proposed algorthm can be appled n general cases, we used another occupancy pattern and conducted dstrbuted actuaton experments. Fgure 1 shows the occupancy pattern and the dstrbuted actuaton results. The Motes could provde a good estmaton. Ths result shows that the algorthm works even f the occupancy pattern changes. Fgure 13 shows the control sgnal profles of the three lghts n the dstrbuted lghtng experment usng a Mote testbed for {s 1,s,s 3 } = {0,1,0}. The parameters were the same as those n Fgure 9. After detectng the occupancy changes, the nodes dmmed the lghts gradually and completed computng the brghtness at 30% of the maxmum brghtness for lghts 1 and 3. The brghtness of lght remaned unchanged. Usng the centralzed algorthm of Equaton (4), we obtaned the control sgnals of the lghts as: { 3 f 1, f, f } = { α,1, α} = {0.3,1,0.3}, (11) whch are almost the same as those n Fgure 11. The RMS error of the calculated control sgnals was and the average communcaton error rate among the Motes was 5.0%. Ths result ndcates that the dstrbuted lghtng control was performed rapdly and precsely usng the Motes mplemented wth the decentralzed algorthm. Fgure 14 shows the control sgnal profles of the three lghts for {s 1,s,s 3 } = {1,0,0}. The control sgnals calculated from the centralzed algorthm are: { f 1, f, f 3} = {1, α /(1 + α α ), α /(1 + α α )} = {1,0.48,0.074}. (1) The RMS error of the calculated control sgnals was and the average communcaton error rate was 10.0%. Fgure 15 shows the control sgnal profles of the three lghts for {s 1,s,s 3 } = {1,0,1}. The control sgnals calculated from the centralzed algorthm are: { 3 f 1, f, f } = {1, α /(1 + α),1} = {1,0.46,1}. (13)

13 Sensors 009, Fgure 13. Expermental dstrbuted lghtng result obtaned usng Mote testbed for {s 1,s,s 3 } = {0,1,0}. Fgure 14. Expermental dstrbuted lghtng result obtaned usng Mote testbed for {s 1,s,s 3 } = {1,0,0}.

14 Sensors 009, Fgure 15. Expermental dstrbuted lghtng result obtaned usng Mote testbed for {s 1,s,s 3 } = {1,0,1}. Fgure 16. Expermental dstrbuted lghtng result obtaned usng Mote testbed for {s 1,s,s 3 } = {1,1,0}.

15 Sensors 009, The RMS error of the calculated control sgnals was and the average communcaton error rate was 5.0%. Fgure 16 shows the control sgnal profles of the three lghts for {s 1,s,s 3 } = {1,1,0}. The control sgnals calculated from the centralzed algorthm are: { 3 f 1, f, f } = {1,1, α} = {1,1,0.3}. (14) The RMS error of the calculated control sgnals was and the average communcaton error rate was 10.0%. These results ndcate that the varous decentralzed lghtng controls were successful when usng the proposed decentralzed algorthm of the wreless sensor/actuator nodes. We attaned the same accuracy as the centralzed algorthm wth a small number of communcatons and computatons because of the large value of the step sze employed n the teratve process. 5. Dscusson The smulaton of the centralzed collaboratve actuaton algorthm revealed that optmal control sgnals can be obtaned when the central server can gather data from all the sensor nodes. Ths algorthm wll be useful when t s used n relatvely small WSANs. On the other hand, the proposed decentralzed collaboratve actuaton algorthm s more scalable n practcal deployment because t does not need a central server. The routng becomes more complcated as the sensor network becomes larger. Ths algorthm s free from such a complcated routng problem. The trade-off between the accuracy of the calculated sgnals and the energy consumed by communcaton s stll a sgnfcant problem n the decentralzed WSANs. We proposed an mproved decentralzed algorthm for fast control sgnal computaton. Experments have ndcated that the number of teratons s reduced to approxmately ten wth approprate step values n the teratve process. We mplemented the algorthm on Motes and evaluated ts feasblty. The Mote employng the decentralzed algorthm provded the same results as the smulatons. The accuracy of computng the control sgnals depends on the step values, the number of teratons, and the communcaton qualty. However, the ncrease n teratons leads drectly to a long computaton tme. In addton, communcaton error s lkely to be nevtable n WSANs. Expermental results ndcated that usng large step values s effectve for computng the control sgnals rapdly and precsely. The average consensus algorthm [16] s closely related to ours. It mnmzes a dsagreement functon to compute the average of the nodes' ntal values. It provdes a consensus mechansm to compute the average n a large network. It s also appled to a varety of networks such as dynamc networks. In our work, on the other hand, the am s not to compute the average but to mnmze the sum of the consumed energy and the spatal roughness of brghtness. And the topology s fxed n the lghtng applcaton. Applyng the proposed algorthm to varous networks remans to be nvestgated. In the proposed dstrbuted actuaton model, t s unnecessary to clarfy the locaton of each sensor node. Each sensor node may have access to nformaton about neghborng nodes. It s best to arrange sensor nodes at regular ntervals and lmt the communcaton range to ther neghbors. One way to recognze neghborng nodes s to use a receved sgnal strength ndcator (RSSI). Ths also remans to be nvestgated.

16 Sensors 009, The smoothness of controlled sgnals depends on model parameter α When α s set at 0, the calculated controlled sgnal s such that only occuped areas are llumnated and other areas are dark. In contrast, when α s set at 1 the calculated control sgnal s such that all areas are llumnated. The parameter depends on whether the purpose of controllng the envronment s to save energy or to mantan user satsfacton. The dstrbuted lghtng experment showed that the autonomous nodes provded the optmal lghtng actuaton wthout a central server. The experment was on a small scale usng only three lghts. However, a larger lght network would be possble, as shown n Fgure 10. These results show that the proposed WSANs are scalable for practcal envronment control systems. In ths work we assumed that the controlled actuators are manly lghts. Other actuators such as ar condtonng systems are applcable, and temperature and humdty can also be controlled. These spatally dstrbuted physcal sgnals are targeted by the proposed WSANs. Our testbed has IR LEDs capable of controllng varous devces easly thus consttutng a versatle controller. We plan to use t to control other actuators. In ths paper, we developed nodes equpped wth sensng and actuaton functons. By contrast, t s possble to construct WSANs consstng of three types of nodes: sensors, actuators and controllers [3]. In such networks, sensors are dstrbuted densely, and actuators and controllers are dstrbuted sparsely. We must buld a heterogeneous communcaton model that ncorporates these dfferent types of nodes. As future work, we plan to develop a testbed that adapts to users actons and preferences. We also plan to employ the proposed algorthm n ths testbed and demonstrate dstrbuted sensng and actuaton that adapts to the users. 6. Conclusons Ths paper descrbed mproved collaboratve sensng and actuaton algorthms for provdng optmal control of lghts n workplaces. In our algorthm, the objectve functon s defned to balance energy savng aganst control sgnal qualty. We proposed a decentralzed algorthm that can autonomously calculate control sgnals wthout a central server. We demonstrated ts accuracy and effcency compared wth the prevously proposed method usng smulatons and Motes. It uses approprate step sze values n the teratve process used for calculatng control sgnals. Expermental results showed that t s useful for provdng accurate and fast computaton because t s dffcult to elmnate communcaton errors. Ths approach enables practcal WSAN deployment because t s easy to mplement and mantan. In addton, we descrbed a testbed for dstrbuted lghtng control based on the decentralzed algorthm. It has IR LEDs for controllng varous devces wrelessly and flexbly. It can be used as a versatle controller for other actuators wth IR detectors. We showed that t acheved optmal lghtng control wthout a central server. In addton, the decentralzed computaton was very fast and precse. The expermental results suggest that ths approach wll allow us to realze a practcal envronment control system. References and Notes 1. Zhao, F.; Gubas, L. Wreless Sensor Networks: An Informaton Processng Approach; Elsever: San Francsco, CA, USA, 004.

17 Sensors 009, Rabbat, M.; Nowak, R. Dstrbuted Optmzaton n Sensor Networks. In Proceedngs of IPSN 04, Berkeley, CA, USA, Aprl 6-7, 004; pp Rabaey, J.M. Low-power Sensor Networks. In Proceedngs of ISSNIP005 Tutoral, Melbourne, Australa, December 5-8, Robomote. Avalable onlne: (accessed on October 0, 009). 5. Coates, M.; Ing, G. Actuator Networks: Dstrbuted Evaluaton of Causal Effect. In Proceedngs of Sgnals, Systems and Computers, Pacfc Grove, CA, USA, November 7-10, 004; pp Taylor, K.; Ward, J.; Gerasmov, V.; James, G. Sensor/Actuator Networks Supportng Agents for Dstrbuted Energy Management. In Proceedngs of 9th Annual IEEE Internatonal Conference on Local Computer Networks (LCN'04), Tampa, FL, USA, November 15-17, 00; pp Zhang, H.; Krogh, B.; Moura, J.M.F.; Zhang, W. Estmaton n Vrtual Sensor-Actuator Arrays Usng Reduced-Order Physcal Models. In Proceedngs of 43rd IEEE Conference on Decson and Control, Atlants, Paradse Island, Bahamas, December 14-17, 004; pp L, S. Wreless Sensor Actuator Network for Lght Montorng and Control Applcaton. In Proceedngs of Consumer Communcatons and Networkng Conference, Las Vegas, NV, USA, January 8-10, 006; pp Sandhu, J.S.; Agogno, A.M.; Agogno, A.K. Wreless Sensor Networks for Commercal Lghtng Control: Decson Makng wth Mult-agent Systems. In Proceedngs of Workng Notes of the AAAI-04 Sensor Networks Workshop, San Jose, CA, USA, July 6, 004; pp Snghv, V.; Krause, A.; Guestrn, C.; Garrett, J.H. Jr.; Matthews, H.S. Intellgent Lght Control usng Sensor Networks. In Proceedngs of SenSys'05, San Dego, CA, USA, November -4, 005; pp Ln, Y.; Megeran, S. Low Cost Dstrbuted Actuaton n Large-scale Ad Hoc Sensor-actuator Networks. In Proceedngs of 005 Internatonal Conference on Wreless Networks, Communcatons and Moble Computng, Mau, HI, USA, 005; pp Nakamura, M.; Sakura, A.; Furubo, S.; Ban, H. Collaboratve Processng n Mote-based Sensor/actuator Networks for Envronment Control Applcaton. Sgnal Proc. 008, 88, Bryson, A.E. Jr.; Ho, Y.-C. Appled Optmal Control; Taylor & Francs: Levttown, PA, USA, Varga, R.S. Matrx Iteratve Analyss; Prentce Hall: Englewood Clffs, NJ, USA, TnyOS. Avalable onlne: (accessed on October 0, 009). 16. Saber, R,O.; Fax, J.A.; Murray, R.M. Consensus and Cooperaton n Networked Mult-Agent Systems. Proc. IEEE 007, 95, by the authors; lcensee Molecular Dversty Preservaton Internatonal, Basel, Swtzerland. Ths artcle s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense (