building environment control with wsan

3596 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 11, NOVEMBER 2010

Building-Environment Control With Wireless Sensorand Actuator Networks: Centralized

Versus DistributedXianghui Cao, Student Member, IEEE, Jiming Chen, Member, IEEE,

Yang Xiao, Senior Member, IEEE, and Youxian Sun

AbstractThis paper considers joint problems of controland communication in wireless sensor and actuator networks(WSANs) for building-environment control systems. In traditionalcontrol systems, centralized control (CC) and distributed con-trol (DC) are two major approaches. However, little work hasbeen done in comparing the two approaches in joint problemsof control and communication, particularly in WSANs servingas components of control loops. In this paper, we develop a CCscheme in which control decisions are made based on globalinformation and a DC scheme which enables distributed actuatorsto make control decisions locally. We also develop methods thatenable wireless communications among system devices compatiblewith the control strategies, and propose a method for reducingpacket-loss rate. We compare the two schemes using simulationsin many aspects. Simulation results show that the DC can achievea comparable control performance of the CC, while the DC is morerobust against packet loss and has lower computational complexitythan the CC. Furthermore, the DC has shorter actuation latencythan the CC under certain conditions.

Index TermsBuilding-environment control, centralized con-trol (CC), distributed control (DC), wireless sensor and actuatornetworks (WSANs).

I. INTRODUCTION

BUILDING-ENVIRONMENT control systems are used forcontrolling the environment of buildings, such as tem-perature, humidity, and illumination, by means of heating, airconditioning, ventilating, lighting, and so forth. There are someavailable commercial products based on wired-communicationtechniques for setting up such systems. However, researcheshave not been well done in wireless sensor and actuator net-works (WSANs), which have the benefits of energy efficiencyand easy deployment. WSANs comprise groups of low-cost

Manuscript received December 31, 2008; revised May 7, 2009; acceptedJuly 4, 2009. Date of publication August 21, 2009; date of current versionOctober 13, 2010. This work was supported in part by the National ScienceFoundation ChinaGuangdong Province Union Project under Grant U0735003,by the National Science Foundation China under Grants 60604029, 60736021,and 60974122, by the 863 High-Tech Project 2007AA041201, and by the 111Projects under Grant B07031. Prof. Xiaos work was supported in part by theU.S. National Science Foundation (NSF) under Grants CCF-0829827, CNS-0716211, and CNS-0737325.

X. Cao, J. Chen, and Y. Sun are with the State Key Laboratory of IndustrialControl Technology, Institute of Industrial Process Control, Zhejiang Univer-sity, Hangzhou 310027, China (e-mail: [email protected]).

Y. Xiao is with the Department of Computer Science, The University ofAlabama, Tuscaloosa, AL 35487 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2009.2029585

and self-organizable wireless sensors and actuators that coop-erate in monitoring and contributing to improve the physicalenvironment. In many situations, single or multiple controllersare involved to collect sensory information, schedule tasks,make control decisions, and coordinate actuators. WSANs havebeen applied for building-environment control systems. In [1],a number of photosensors and actuators (dimmable lightingballasts mounted on the ceilings) are used to satisfy userpreferences in an intelligent lighting system for an office. Thegoal of such a system is to adjust the actuators to providelighting-comfort levels while saving electricity consumption.Sensors sense their surroundings and provide real-time illumi-nance measurements. A control unit analyzes sensor readings,evaluates current system states such as user preferences, elec-tricity rates, if required, and then makes decisions to adjust theoutput of actuators. Humidity, ventilation, and air-conditioningsystems (with the main components as user preferences, sen-sors, actuators, and controllers) for buildings, integrated withWSANs, take an important role in saving electrical powernowadays [2].

To illustrate the usage of WSANs in building-environmentcontrol systems, let us consider an example of controlling envi-ronment temperature of an office shown in Fig. 1. Suppose thatsix air conditioners (actuators) are uniformly installed, wheretemperature inside the office rests at 20 C. A number of sensorsare deployed to measure the temperature. The actuators andsensors are equipped with wireless communication capabilitiesso that they are able to form a WSAN. Because the doors areopened, the distribution of the temperature changes, as shownin Fig. 1. One of the goals in interest is to find a better ap-proach to maintain 20 C everywhere inside the office with theWSAN. If the actuators only care about their local environmenttemperature, our simulations [see Fig. 5(a)] indicate that theaforementioned goal is difficult to be achieved. Therefore, newstrategies for control, networking, communication, and taskscheduling are necessary. We propose a three-tier design (fromthe bottom to the top) for such a WSAN.

1) Network tier: It provides networking services to a con-troller, if any, actuators, and sensors with wireless-communication protocols such as medium-access control(MAC), routing, time synchronization, security, etc.

2) Control tier: It is a closed control loop composedof the controller, if any, actuators, physical envi-ronment as plant, and sensors as transmitters. It is

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CAO et al.: BUILDING-ENVIRONMENT CONTROL WITH WIRELESS SENSOR AND ACTUATOR NETWORKS 3597

Fig. 1. Example of a WSAN for temperature control. The contour linesillustrate the temperature distribution inside the office.

responsible for gathering sensor measurements and ac-tuator states, estimating network states, making controldecisions, and coordinating the actuators. Its operationsare supported by the Network tier while the controlobjective is specified by the User interface. Comparedwith wired-communication networks, wireless networkshave high packet-loss rates and larger delays. Therefore,information at control-decision unit(s) is unreliable andincomplete. This becomes a top challenge and should beseriously treated at this tier.

3) User interface: This tier defines control objectives andinteracts with network users.

We focus on the first two tiers and propose two distinctschemes1a centralized control (CC) scheme and a distributedcontrol (DC) scheme. In the CC, there is a centralized controllerthat gathers packets from sensors and actuators, makes controldecisions based on all the received information, and dispatchescommands to coordinate actuators. In the DC, based on localinformation, control decisions are made locally by each actua-tors, such as the actuator denoted as Ai does, as shown in Fig. 1.Detailed network operations are presented in Sections IV andV for the CC and the DC, respectively. In the literature, thedistributed concept has been introduced into wireless sensornetworks (WSNs) for target tracking [4], [5] and transmissionpower control [6]. It was shown that it is successful and superiorover centralized schemes in many aspects. In our case, althoughthe CC is able to have global information and can be appliedwith globally optimal control laws, it may not outperform theDC when unreliable wireless communication and large networkscalability are concerned.

The main contributions in this paper aside from our earlywork in [3] are explained as follows. First, we develop theo-retical models for network devices and the environment. Our

1The earlier work had been presented in IEEE ICC 2008 [3].

models are generic in the sense that they are easily appliedto control other building environment. Second, based on thecontrol algorithms in [3], we design two task-scheduling mech-anisms for the CC and DC, respectively, in order to facilitatecontrol strategies and keep the devices operating synchro-nously. Third, in both control schemes, the information at thecontrol decision unit(s) (including those transmitted from thecontroller to the actuators in the CC) should be enough forestimation and calculation (and for conducting actuation). Thisrequires that packet-loss rate is low. To this end, we propose aneffective mechanism based on an idea of separating concurrentand successive packet transmissions to avoid packet collisionsand reduce packet-loss rates. Fourth, we study the effects ofactuation latency on system overall performances using simu-lations that are developed in OMNeT++ [7] with IEEE 802.15.4standard [8] being integrated. In the simulations, the CC and theDC are compared in terms of not only control performance butalso energy efficiency, computational complexity, and packet-loss rate.

The rest of this paper is organized as follows. Related work ispresented in Section II. We then develop the system models inSection III. Sections IV and V present how the control systemsoperate for the CC and the DC, respectively. We discuss howto reduce packet-loss rate and actuation latencies for the twoschemes in the sections that follow Section V. Simulationresults are presented in Section VIII. Finally, Section IX con-cludes this paper.

II. RELATED WORK

Recalling our three-tier design described previously, re-searchers have made some contributions to the Network tiersuch as [9][11]. For the User Interface and Control tier,[12] considered filtering user commands which may harmthe system operation. In the literature, for the Control tier, afuzzy-logic control is implemented for building illuminationand temperature control in [13]. A novel multiagent controlsystem for managing the comfort level of building environmentis proposed in [14]. However, the conventional methods formodeling and controlling building environment may becomeunpractical when the control-system loops are closed by theWSANs, in which unreliable and incomplete information andnetwork behaviors, such as energy efficiency, should be paidenough attention. In this paper, we focus on the Control tierand making the Network tier compatible with the controlstrategies.

The introduction of intelligent actuators to WSNs leveragessuch a monitoring-oriented system to enable interaction be-tween human and the physical world. In return, designing thecontrol strategy is a new challenging issue. Sinopoli et al. intro-duced a control problem involved in WSANs motivated by thedistributed pursuitevasion game [15], and presented researchchallenges within a DC system without global information.They also proposed a hierarchical control model, including alower continuous component and a higher discrete component.A distributed-actuation scheme was discussed in [16]. Becauseof the superiority of energy savings of a distributed-actuationscheme over a centralized one, [16] emphasized on a distributed




system and developed several useful actuation strategies basedon simulations. Nakamura et al. proposed a sensor/actuatornetwork with collaborative sensing and actuation for lightingcontrol [17]. The authors also discussed algorithms for decidingcontrol signals in both centralized and decentralized ways.Marti et al. proposed a joint design of networked controllersand message scheduling in order to manage overall quality ofservice, with consideration of limited communication resources[18]. Robinson and Kumar addressed the optimal controllerlocation in a wirelessly connected control system [19]. Theyalso proposed the optimal control strategy at that location.However, they focus on designing either only CC or onlyDC, while little work has been done that brings both controlmethods together into consideration. In this paper, these twodistinct approaches are brought into our designs and comparedwith building-environment control systems by taking wireless-communication characteristics, such as packet loss, intoaccount.

III. SYSTEM MODELS

Let EnV be the building-environment variable of our con-cern, such as temperature and humidity in an office. Sensorsare deployed to measure EnV , while actuators are employed toaffect the distribution of EnV . We suppose that there are totallyns sensors and na actuators2, and the actuators influencingranges3 together cover the area of our concern. We assume that,for both the CC and the DC, control proceeds with step length(time period) T , and that the synchronization within the wholenetwork has been achieved.

A. Actuator and Sensor Models

Let Ai denote the ith actuator, xi denote its output whichinfluences its ambient distribution of EnV , and ui denote thecontrol output that is used to adjust Ais actuation, where i =1, . . . , na. At each step k, Ai is modeled by

xi[k] = xi[k 1] + vi[k]ui[k] + i[k] (1)

where i is a noise. vi[k] is a Bernoulli random variable4(P (vi[k] = 1) = vi) indicating whether the packet that con-tains ui[k] is successfully received by Ai.

vi[k] ={

0, if Ai does not receive ui[k] in step k1, otherwise. (2)

We rewrite (1) in matrix form

x[k] = x[k 1] + v[k]u[k] + [k] (3)

2The sensors and actuators are numbered by {1, . . . , ns} and {1, . . . , na},respectively.

3We assume that each actuator has an influencing range inside which itsactuation has an effect on EnV . This range is either geographically or logicallydetermined.

4In the literature, packet loss is modeled in several ways among which, usingBernoulli random variable is a widely accepted approach, such as in [20][22].

where x = [x1, . . . , xna ]T , u = [u1, . . . , una ]T , =[1, . . . , na ]

T. Let

v =

v1 . .

.

vna

v =

v1 . .

.

vna

. (4)

Due to the actuators physical constraints, its output cannotchange freely within the period T . Thus, u is bounded. Let u [u, u].

Let Sj denote the jth sensor and yj denote the actual value ofthe EnV at Sj . We assume that Sjs measurement mj differsyj by a measurement noise j . So, at kth step

mj [k] = yj [k] + j [k] j = 1, . . . , ns. (5)Similar to u, x, and , we define m, y, and .

B. Environment Model

To facilitate our presentation, the environment model isdescribed with the example of a building-temperature control.In a continuous time domain, the increment of yj at time t iscaused by the heat transferred from actuators and surroundingenvironment as occupied by other sensors. Assume that suchrelation is simply linear. Thus, we have

dyjdt

=

1lns,l =jlj(yl yj) +

1lna

lj(xl yj) (6)

where lj and lj are coefficients relating to heat-transferefficiency. The previous equation can be written in matrix formas follows:

dy(t)dt

= y(t) + x(t) (7)

where Rnsns and Rnsna .Assume that x is constant within each step, i.e., x(t) x[k],

t [(k 1)T, kT ). Now, (7) has following solution:y(t0 + t) = ety(t0) + 1(et 1)x[k], t [0, T )

(8)where t0 = (k 1)T . Since the building-environment temper-ature does not have step changes, i.e., y(t) is continuous at timekT , and, thus, we have

y(kT ) = eT y ((k 1)T ) + 1(eT 1)x[k]. (9)Since , , T are coefficients or constants, taking the envi-

ronment noise into account, the previous equation becomes

y[k] = Cy[k 1] + Dx[k] + [k] (10)where C = eT and D = 1(eT 1). A balanced case:1 j ns if yl = yj , 1 l ns, and all actuators areturned off, i.e., lj = 0, 1 l na, then dyj/dt = 0. Thus, notransferring happens, and the environment reaches a balancedstate. By substituting the aforementioned conditions to (10) andignoring the noise , we can say that the summation of everyrow of matrix C equals one. An exception is that C = 0.







Fig. 2. Flow chart of centralized control. The controller, actuators, and sensors are connected by wireless links with different packet-loss rates.

Fig. 3. Tasks scheduling of centralized control.

Remark 1: The aforementioned environment model can alsobe applied for other environment variables, e.g., humidity. Notethat in the case of lighting control, C = 0 because there is notransferring of light intensity. Equation (10) describes a genericlinear-control-system model, based on which the followingmechanisms are developed. For building-environment-controlapplications, our mechanisms can be generally applied as longas the concerning environment models are described by (10).

C. Control ObjectiveThe user-preferred value of EnV at the jth-sensor place is

denoted by pj , j = 1, . . . , ns. Define p = [p1, . . . , pns ]T . Thebasic control objective is to minimize the difference betweenuser requirements and system output y[k]. Let e[k] = p y[k].We define the control objective function as

[k] = eT [k]e[k]. (11)The control objective is to minimize [k].

IV. CC SCHEME

The controllers task is to, first, get a knowledge of thesystem current states and, then, design the control output uby which it informs the appropriate actuators. The sensors andactuators should first send their measurements m and states f ,respectively, to the controller. These two kinds of feedbacks are

necessary because of the following: 1) x[k] is unknown to thecontroller, although x[0] and u[k] are known, since v[k] and[k] can be time variant, and 2) y[k] is also unknown, eventhough y[0] is known, since x[k] and [k] are unknown and aretime variant. The feedback information the controller receivedin step k is described by

f [k] = vac[k] (x[k] + [k]) (12)m[k] = vsc[k](y[k] + [k]) (13)

where vac and vsc are similarly defined as v in (3). and [see(5)] are noises.

Now, we are able to see the flowchart of the CC as shownin Fig. 2, where the Plant stands for the environment of theoffice. The controller takes p and the feedbacks to estimatethe required information and then makes decisions and sendscommand packets to the actuators to adjust their performances.

A. Tasks Scheduling

If the Network tier works properly, the control loop operatesstep by step. The details of each step of the CC are describednext and shown in Fig. 3.

1) Each sensor Sj : At the beginning of each step, it startssensing ambient environment and measuring EnV . Itthen packs up the measurements and reports them to thecontroller. After that and before the next step, it rests in





an idle state unless there are other network packets thatneed to be forwarded.

2) Each actuator Ai: When step k begins, it starts feedingits state xi[k 1] back to the controller and also startswaiting for the controllers command until the time periodtca,timeout expires. If the command packet containingui[k] is successfully received before tca,timeout expires, Aichanges its output accordingly. Otherwise, Ai maintainsits previous step output.

3) Centralized controller: It waits a period of tcc,timeout forpackets from sensors and actuators. It then estimates anddecides the control output based on the information itreceived during tcc,timeout. It packs the control outputs uiup to command packets for each of the actuators. Thecommand packets will be dispatched to the correspondingactuators through the network afterward. Let tccalc be thetime cost by estimating and deciding control.

B. Estimation and Control Decision

When the controller starts to estimate the systemstates at step k, the information which it knows isI[k]={p, u(k1), f (k),m(k), v(k)sc , v(k)ac , x(k1), y(k1)}, where(k)={[0], . . . , [k]} . x[k] =E{x[k]|I[k]}, y[k] =E{y[k]|I[k]}. In [3], we have discussed about how theestimations are developed using Kalman filter which has beenrecently studied for wireless-network estimation that suffersfrom packet loss and delay [20], [21]. Based on the results ofx[k] and y[k], we can estimate the control objective function,i.e., [k] = E{[k]|I[k]}. Then we will find that the optimalcontrol can be obtained by solving a quadratic programmingproblem which is shown by{

Minimize : uT [k]Qu[k] 2uT [k]z[k]s.t. u[k] [u, u] (14)

Q = vDTDv + (v v2)G(DTD) (15)z[k] = vDT (p Cy[k 1]Dx[k 1]) (16)

where matrix M , G(M) represents a matrix obtained from Mby setting all nondiagonal entries to zero.

V. DC SCHEME

In the DC, control decisions are made by each of the actu-ators based on local information, and no centralized controlleris required anymore. The system models are the same as thosedescribed in Section III except that vi 1. Let us first define In-fluenced sensors as the group of sensors influenced by the sameactuator. For Ai, its influenced sensors are denoted by set SAi .Define Responsible actuators as the group of actuators whichinfluence the same sensor. For Sj , its responsible actuators aredenoted by set ASj . ASj is the number of actuators in ASj .

The control loop for the DC also operates step by step withthe period T , as shown in Fig. 4.

1) Each sensor Sj : It performs similarly to the sensors in theCC, but it reports its measurements only to its responsibleactuators belonging to ASj .

Fig. 4. Tasks scheduling of distributed control.

2) Each actuator Ai: It waits a period of tdc,timeout forpackets from its influenced sensors SAi . It then estimatesand decides its control output ui based on that outputaccording to the decision it has made. Similar to tccalc,we define tdcalc.

The control strategy is designed using the gradient descentmethod. Define the learning error after step k as

[k] =12

(p y[k])T (p y[k]) . (17)

[k] can be estimated ([k] denotes the estimation results)by using the estimates of each ej [k] in the way described in [3].Then, by applying the gradient descent method, we can get asolution for u[k] as follows:

u[k + 1] = u[k]

[k] + u[k] (18)

where e[k] is defined before (11). is called the learning-step length. The term u[k] is introduced to compensate theovershooting caused by large and accelerate the objective-function converging speed. Let dji be the (j, i)th entry ofD, and let ej [k] be the estimate of ej [k]. For each Ai, i {1, . . . , na}, its control output ui[k] can be obtained by

ui[k] = (1 + )ui[k 1] ui[k 2] + nsj=1

djiej [k]

xi[k 1] + (1 + )xi[k 2] xi[k 3]. (19)

Remark 2: Existing methods, such as theproportionalintegralderivative control and fuzzy control,might also be used to design the CC. However, when thecontrol loop is closed by WSANs, such methods should becarefully redesigned to cope with the unreliable and incompleteinformation at the controller, e.g., [23]. As for designing the DCin which control is performed by each of the actuators, thereseem few methods off the shelf that not only are distributed butalso account for the unreliable and incomplete information. Theproposed DC strategy is based on the commonly used gradientdescent method. Moreover, the task-scheduling mechanismsand communication processes are generic for both centralizedand distributed methods.







Fig. 5. (a) Evolutions of the control objective function [k] in case 1: actuators do not join and form WSAN. Each of them performs as if no other sensorsor actuators exist; case 2 and case 3: centralized control and distributed control are applied with approximately 60% packet-loss rates (on average), respectively.(b) Performance comparison between centralized control and distributed control schemes with TSM. (c) Effect of and on DC performances. (d) Controleffort comparison. LR is the average packet-loss rate (average is taken over all communication pairs). (e) and (f) CPU and radio costs of each sensor within onecontrol step with regard to the numbers of sensors and actuators. (g) Energy cost for each sensor with regard to average number of responsible actuators, ns = 25,na = 9. (h) Computational complexity of centralized control.

VI. REDUCING PACKET-LOSS RATE

Packet loss directly harms the estimation and control de-cision. In the CC, packet loss also prevents actuators fromperforming actuation that the controller expected. It is shownby simulations in Fig. 5(a) [compare with Fig. 5(b)] that packetloss not only deteriorates the final control achievements butalso slows down the speed of approaching the control goal forboth the CC and the DC. Taking the CC, for instance, if allthe sensors begin to report their measurements exactly at thesame time, the network will soon become congested, and manypackets may get lost. Such situation takes place at the beginningof each control step in both the CC and the DC. Moreover,we also witness packet loss when the controller dispatchescommands (in the CC), and the sensors report measurementsto responsible actuators (in the DC) without spacing successivetransmissions during simulations. Therefore, we propose thefollowing transmission separation mechanism (TSM).

We let the sensors perform sensing explicitly at the beginningof each step but report their measurements one after another,in order to avoid simultaneous reporting. For the CC, the timeperiod tcc,timeout is divided into (ns + na) equal slots, each withduration c, as shown in Fig. 3. Thus, in step k, Sj starts report-ing its measurement at the time (j 1) c + (k 1)T , whileAi starts reporting at the time ((i 1) + ns) c + (k 1)T .For the DC, the design is similar to the CC: tdc,timeout is equallydivided into ns slots, and the sensors start reporting one by one.Similarly, to make space between successive transmissions, thetime period for the controller to dispatch commands (in the CC)and the time period for each sensor Sj to report measurementsto all actuators in ASj (in the DC) are further divided equallyinto na slots and ASj slots, respectively. See Figs. 3 and 4.

TSM does not harm the synchronization. We may expect thatthe divided slots are long enough so that the delivery (fromoriginal sending to final receiving) of each packet is separatedfrom one another, and, hence, we may achieve as low packet-loss rate as possible.

TSM provides a simple way of reducing packet-loss rate.However, the dividing of time slots to ease heavily contend-ing or separate successive transmissions is much complicatedand should take cross-layer design of MAC and routing intoaccount. For any sensor (or actuator, controller), the time slotassigned to it is expected to embrace the transmission of itsoutgoing packet. However, the transmission successfulness isvulnerable to many factors, such as the number of its neighbors,the multihop path length to the packets destination, and packetlength. These are beyond the scope of this paper, and we justtake the TSM to facilitate the control systems.

VII. ACTUATION LATENCY

In the CC, tca,timeout can be also understood as the periodfrom when the feedback processes start to when the actuatorschange their output according to control output. At each step,the feedback information which the controller receives is theinformation a tcc,timeout ago. Moreover, the actuators do notchange their output instantly as the control output has beendecided. Therefore, the actuation changes according to theinformation that is generated a period of tca,timeout ago. Thisinformation may be totally out of date and should not berelied on. Hence, the communication real-timeliness has greatimpact on the control performance. To this end, a P-CSMA/CAprotocol is designed to meet real-time requirements [24]. An



optimal estimation and control is proposed to cope with randompacket delays [21]. We define the actuation latency of the CC asthe period tca,timeout. Similarly, we define the actuation latencyof the DC as tda,timeout. They are very important to the networkcommunication real-timeliness and, hence, the timeliness of theestimations, control, and actuation. In this sense, both of themshould be as small as possible.

Proposition 1: If we want to separate the deliveries of allpackets, tda,timeout can be designed to be less than tca,timeout if

AS 0 if Si and Sj are adjacentso that their environment temperature are correlated, otherwise,ci,j = 0. ci,i = 1

nsj=1,j =i ci,j . The noises , , , and

are assumed to be white Gaussian with zero means. Supposethat the temperature distribution is initially random because of

door opening. Our aim is to maintain the temperature to be20 C at each of the sensor places.

The simulation platform is developed using the combinationof OMNeT++ tool [7] and Matlab. Only the tasks of estimationand control decision making are carried in Matlab. The protocoland standard of the devices used to perform wireless communi-cations are the following: The Network tier uses a GEAR-based[25] routing protocol and the MAC and PHY layers use IEEE802.15.4 standard [8] and the 2.4-GHz band. Constants thatwere used during our simulations are the following: [u, u] =[5, 5], T = 10 s, tcc,timeout = 0.2 s, tca,timeout = 0.25 s, andtda,timeout = 0.17 s. The parameters for running the DC are = 0.8 and = 0.5.

A. Control PerformancesIf no control strategy is adopted by the actuators and, thus,

each actuator controls its ambient environment as if no othersensors or actuators exist, our control objective to maintainthe temperature of the office is hard to be realized, as shownin Fig. 5(a). Fig. 5(b) shows the simulation results of theperformances of the CC and the DC. It can be seen that the CCstabilizes the control objective function in less than ten steps(100 s), while the system under the DC first oscillates to someextents and, finally, becomes stable after about 20 steps. Inother words, the system under the CC converges much quicklythan under the DC because the former runs the optimal controlstrategy at each step with the controllers global knowledge ateach step, while the latter pursuits the optima step by step.

Without the TSM, the overall average packet-loss rates are56.4% for the CC and 39.3% for the DC. However, they cometo about 20% for both schemes when TSM is applied. We lettcc,timeout = 0.06 s, t

ca,timeout = 0.08 s, and tda,timeout = 0.07 s,

so both aforementioned rates come to about 60%. ComparingFig. 5(a) with Fig. 5(b) reveals that the control performances ofboth schemes under 60% average packet-loss rate are inferior interms of converging speed to those under 20%. Besides, the DCis more robust than the CC against packet loss since it stabilizes[k], while the CC does not.

The performance of the DC depends on the learning-steplength which relates to the speed of lessening the learningerror [k]. Seen from Fig. 5(c), if is small, such as 0.2, theconverging speed of the objective function will be muchslower. In particular, if = 0, will stay at a high value.Other simulations show that the actuators will perform violentactuation and, as a result, the system becomes even unstablewhen is too large, e.g., = 2.0. is introduced to compensatethe control overshooting, stabilize the system from oscillating,and accelerate the system converging speed. Observed fromFig. 5(c), converges much slowly without . However, thesystem become unstable when is smaller than 0.9.

Usually, the termk

i=1 uT [i]u[i] (Fig. 5(d) plots its average

values over na) is another important metric of the controlperformance. It measures the effort the controller (or actuatorsin the DC case) dedicates to adjust the actuators performances.This term is effected by packet loss as shown by Fig. 5(d).Although the CC is able to achieve the control objective withless effort than the DC, if both were without packet loss, the


former is more complicated in control than the latter if theyperform under the same nonzero packet-loss rate. In addition,the increase of the packet-loss rate may even make the controlsystem unstable. For example, when the packet-loss rate is 40%,as shown by Fig. 5(d), the CC spends continuously growingeffort which corresponds to the fact that the objective functiondoes not converge in this case. Therefore, the DC is more robustagainst packet loss than the CC.

B. Energy EfficiencyThe controller and the actuators can have more powerful

energy supplies than the sensors which are only battery pow-ered. Therefore, the energy efficiency of the sensors is of greatimportance, which may further determine the lifetime of thewhole system. Sensing (by sensor board), processing (by CPUand peripheral components), and communication (by radio) arethree major kinds of energy consumption of a sensor. Sincethe sensing cost is nearly constant and does not relate to othersensors or actuators, we only consider the energy consumedby the radio and the CPU. We adjust tcc,timeout, tca,timeout, andtda,timeout to let every packet delivery be successful so that theeffect of packet loss can be eliminated. The simulation resultsare shown in Fig. 5(e) and (f). The power supplied when theCPU is in active, idle, and power-save modes are 8.0 mA,4.2 mA, and 10 A, respectively, according to ATmega128(working on 8 MHz) data sheet [26]. The power values suppliedwhen the radio is idle, receiving, and transmitting are 0.426,18.8, and 17.4 mA, respectively, according to CC24240 datasheet [27]. We observe that the amount of energy consumedby the CPU grows as the number of sensors ns increases. Itbehaves similarly as na grows, too. However, the increase ofna raises the CPUs energy consumption in the DC schememuch greater than that in the CC scheme. We also have similarobservations from Fig. 5(f). Moreover, seen from Fig. 5(f), theamount of energy consumed by the radio in the DC scheme islarger than that in the CC scheme in most cases. However, fromFig. 5(g), we observe that the amount of energy consumed byboth CPU and radio in the DC scheme relies on the averagenumber of responsible actuators AS which is defined after(20). Obviously, AS relates to the deployment density of theactuators. As shown by this figure, if we are able to keep thedensity of actuators small enough, each sensor can be moreenergy efficient in the DC scheme than in the CC scheme.

C. Computational Complexity

The computational complexities at the control decisionunit(s) of CC and DC directly relate to tdcalc and tccalc as dis-cussed in Section VII and, hence, have effects on the actuationlatencies. Insights into the estimation and control processesof the CC reveal that the computational complexity for thecontroller to estimate and decide at each step is on the orderO(n3s) +O(n3a). Normally, na ns, so, the complexity comeson the order O(n3s). Simulation results are shown in Fig. 5(h),where we use the time tccalc (see Fig. 3), which is measured inMatlab, to describe the complexity of the CC. The polynomialfitting line in this figure reveals the O(n3s) order of that com-

Fig. 6. Average packet-loss rates (see definitions in Section 8.4).In (b), tcc,timeout is fixed at 0.2s.

plexity. The computational complexity of a single actuator inthe DC is always too small and is not plotted.

D. Packet-Loss Rate

In a single step, we define the following average packet-loss rates: LRsc and LRac for the communications from sen-sors and actuators to controller within tcc,timeout in the CC,respectively; LRac for the communications from controller toactuators within (tca,timeout tcc,timeout) in the CC; LRsa forthe communications from sensors to actuators within tda,timeoutin the DC. The simulation results are shown in Fig. 6(a) and(b). We find that in order to let the average packet-loss ratesto about 20% (as used for the simulations in this paper andin [3]), we should make tcc,timeout 0.2 s, tca,timeout 0.25 s,and tda,timeout 0.17 s. Moreover, in order to separate packetdeliveries, tca,timeout 0.7 s, and tda,timeout 0.5 s. The actua-tion latency of the DC is less than that of the CC. This supportsProposition 1.

IX. CONCLUSION

We have presented the models for building-environmentcontrol using WSANs. Two control schemes are described indetail: a CC scheme in which control decisions are made by asingle centralized controller based on global information and aDC scheme in which control decisions are made by distributedactuators based on local information. They differ from eachother in many aspects.

1) Both the CC and the DC are able to achieve our controlobjective, finally. The CC, however, outperforms the DCin terms of s converging speed.

2) In the CC, transmission failure of control-command pack-ets prevents the actuators from being undercontrolled,although, such situations does not happen in the DC, sincecontrol decisions are directly applied at the actuators. TheDC is more robust against packet loss than the CC.

3) With TSM applied, simulation results indicate that theactuation latency of the DC is less than that of the CCwhen the average packet-loss rates are the same for theCC and the DC.

4) The energy consumption due to radio communicationsof a sensor grows faster as the network scale (numberof sensors) increases in the DC than that in the CC.


However, if the actuators are deployed loosely enough,the total amount of energy consumed by a sensor in theDC scheme can still be less than that in the CC scheme.

5) The CC is inappropriate for large-scaled WSANs, at least,because its computational complexity grows tremen-dously with the network scale, whereas, the DC hasshown excellent scalability because control relies only onlocal communication.

However, the DC suffers from the fact that its control perfor-mance is sensitive to the parameters and . In our future work,we will study them and try to make them adaptive for differentapplication cases.

ACKNOWLEDGMENT

The authors would like to thank the Associate Editor andthe anonymous reviewers for their valuable comments andsuggestions that have significantly improved the quality of thispaper.

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Xianghui Cao (S08) received the B.S. degreein automation from Chukochen Honors College,Zhejiang University, Hangzhou, China, in 2006. Heis currently working toward the Ph.D. degree inthe Department of Control Science and Engineering,Zhejiang University.

From December 2007 to June 2009, he was aVisiting Scholar with the Department of ComputerScience, The University of Alabama, Tuscaloosa.His research areas are data analysis and processingin wireless-sensor networks, network estimation and

control, and distributed control with wireless sensor/actuator networks.Mr. Cao was a reviewer for several journals including IEEE TRANSAC-

TIONS ON INDUSTRIAL ELECTRONICS. He served as TPC member for IEEEWiMob 2009.

Jiming Chen (M08) received the Ph.D. degree incontrol science and engineering from Zhejiang Uni-versity, Hangzhou, China, in 2005.

He was a Visiting Scholar with the Universityof Waterloo, INRIA, and National University ofSingapore, Singapore. He is currently an AssociateProfessor with the Institute of Industrial ProcessControl, State Key Laboratory of Industrial ControlTechnology, Zhejiang University. He leads a group ofnetworked sensing and control, Zhejiang University.He serves as Associate Editor, International Journal

of Communication System, Ad Hoc & Sensor Wireless Networks, an interna-tional journal, Journal of Computers, etc., and was Guest Editor of WirelessCommunication and Mobile Computing. He has published over 50 peer-reviewed papers. His research interests include estimation and control targettracking and optimization in sensor networks sensor and actuator networks.

Dr. Chen currently serves as General Symposia Cochairman of IWCMC2009 and is the WiCON 2010 MAC track Cochairman.


Yang Xiao (S98M01SM04) received the B.S.and M.S. degrees from Jilin University, Jilin, China,in 1989 and 1991, respectively, and the M.S. andPh.D. degrees in computer science and engineeringfrom Wright State University, Dayton, OH, in 2000and 2001, respectively.

He worked with Micro Linear as a Medium AccessControl Architect involving the IEEE 802.11 stan-dard enhancement work before he joined the Depart-ment of Computer Science, University of Memphis,Memphis, TN, in 2002. He is currently with the De-

partment of Computer Science at The University of Alabama, Tuscaloosa. Hecurrently serves as Editor-in-Chief for the International Journal of Security andNetworks, the International Journal of Sensor Networks, and the InternationalJournal of Telemedicine and Applications. His research areas are security,telemedicine, robot, sensor networks, and wireless networks. He has publishedmore than 300 papers in major journals and refereed conference proceedingsand book chapters related to these research areas.

Dr. Xiao was a voting member of IEEE 802.11 Working Group from 2001 to2004. He serves as an Associate Editor for several journals, including the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY.

Youxian Sun received the Diploma degree fromthe Department of Chemical Engineering, ZhejiangUniversity, Hangzhou, China, in 1964.

He joined the Department of Chemical Engineer-ing, Zhejiang University, in 1964. From 1984 to1987, he was an Alexander Von Humboldt ResearchFellow and Visiting Associate Professor with theUniversity of Stuttgart, Stuttgart, Germany. He hasbeen a full Professor at Zhejiang University, since1988. In 1995, he was elected to be an Academicianof Chinese Academy of Engineering. His present

research interests include modeling, control and optimization of complexsystems, and robust control design and its application. He is the author andcoauthor of 450 journal and conference papers. He is currently the Director ofInstitute of Industrial Process Control and national engineering research centerof industrial automation, Zhejiang University.

Prof. Sun also serves as Vice-Chairman of IFAC Pulp and Paper Committee,President of Chinese Association of Automation, and Vice-President of ChinaInstrument and Control Society.

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