Computer Aided Engineering of Cyber-Physical Information Gathering and Utilizing Systems

Transcription

1 Computer Aded Engneerng of Cyber-Physcal Informaton Gatherng and Utlzng Systems Alfred P. DeFonzo, Anthony P. Hopf Department of Electrcal and Computer Engneerng Unversty of Massachusetts Amherst Amherst, MA USA emal: Abstract Engneerng Cyber-physcal nformaton gatherng and utlzng systems(cigus) presents the systems engneer wth a dffcult, mult-crteron, mult-objectve decson problem. Research, development and desgn s done over many dscplnes, across many domans, each wth ther specfc models. Systems engneers are expected to provde a common level of communcaton amongst the domans to promote convergence to a desgn. We present novel nformaton measures that enable combnaton of the underlyng doman specfc subsystems parameters n a way that makes the nformaton yeld of the system ntellgble to decson makers and doman experts. These measures enable, for the frst tme, the applcaton of mult-objectve evolutonary algorthms and end-to-end computer aded engneerng of CIGUS. Our novel approach s valdated and verfed through the applcaton and drect comparson of smulated and expermental results of state-ofthe-art weather radar network test bed desgns. The approach resulted n Pareto optmal pont wthn an average of 10% of the actual case study desgn parameters and wthn 25% of the Pareto deal pont. No addtonal parameters beyond the underlyng doman parameters were ntroduced. Ths demonstrates that the computatonally aded engneerng approach presented n ths work facltates engneerng feasblty decsons and the subsequent evoluton of the engneered systems n way that reduces cost and effort. Index Terms nformaton gatherng and utlzng systems, cyberphyscal, network sensors, mult-objectve problem, optmzaton. I. INTRODUCTION Interest n the engneerng of cyber-physcal nformaton gatherng and utlzng systems (CIGUS) has burgeoned n part due to the prolferaton of wreless technology [1] and n part due to the growng demand for ntellgble nformaton. Such systems are complcated, wth herarches of nterfaces contanng underlyng complexty. They often nvolve dstrbuted network sensors. The confguraton can be dynamc, statc and adaptve. Increasngly they nvolve real tme collaboraton among agents of varyng degrees of autonomy. The nterface of hgh yeld systems often hdes underlyng subsystem complexty whch pose new challenges to systems engneerng[2]. Systems engneers are expected to provde a common level of communcaton amongst the domans of expertse that enable research, development and desgn of the system to converge. As the domans become hghly optmzed, the language and models become so specalzed that t becomes extremely dffcult to communcate across the domans. Pror to ths work there was no practcal and well founded way to combne the parameters of the underlyng subsystems n order to represent the overall ntellgble nformaton yeld. Moreover, n order for systems engneers to make the multcrtera tradeoffs and optmzatons requred for such systems, t s necessary to ntroduce new sets of objectve functons wthout whch exstng mult-objectve evolutonary algorthms[3], [4], [5], [6] can not be appled to CIGUS. In the case of CIGUS, specfc doman experts do the component subsystem desgn and subsequent modelng. Each of these doman specfc subsystem models are developed n ther partcular doman language. Sgnal processng and communcaton models are essental to these systems. Weather Radar networks are a classc example. The sub-domans models nvolved n the systems engneerng nclude; models of the component radars and ther subsystems[7], network[8], sgnal processng[9], [10], and control[11]. What they have lacked s a systematc approach to overall optmzaton supportng the decson makng process. The obstacle s combnng parameters from dfferent domans of expertse. The systems engneers ablty to provde a level of abstracton that captures the entre system desgn problem at all levels wll determne how quckly, or slowly, the desgn wll converge to meet the requrements and how rapdly the systems wll evolve. Clearly, for CIGUS, the underlyng parameters and measures should resolve themselves n terms of the essental product: ntellgble and useful nformaton. Moreover, CIGUS may be system of systems wth uncertan and evolvng requrements. Decsons made at multple levels present a dffcult mult-crtera, or mult-objectve, decson problem. The systems engneer s presented wth a dffcult task of provdng the decson makers wth the nformaton needed to support nvestment nto further system evoluton and development. By ntroducng nformaton measures we are able to express the qualty of the system n terms of more generally understood notons such as accuracy, precson, and bt rates as objectve functons. We show that these objectve functons, whch encapsulate underlyng doman specfc parameters wthout ntroducng addtonal parameters. These can be combned wth cost and throughput functons n a way that enables the applcaton of state-of-the-art mult-objectve evolutonary algorthms and automated decson support tools. Moreover, the predctons of ths analyss can be drectly compared wth expermental data from test beds. One recent state-of-the-art weather network test bed, the Collaboratve Adaptve Sensng of the Atmosphere (CASA) Integrated Project 1 (IP1), enables the comparson of smulatons and expermental results presented n ths paper and n more detal elsewhere. II. APPROACH To capture the salence of the engneered system, the systems engneer must separate the doman experts concerns, whch are pursuant to provdng objectve content from the decson makers concerns, whch are pursuant to ensurng that hgher-level requrements are satsfed. Whle not conceved as such, a non-obvous example, rch n engneerng challenges s the recently deployed the CASA IP1[12] expermental network of weather radars. The development s drected toward demonstraton of the engneerng feasblty of an end-to-end (TRL 6) [13] herarchcal emergency response and real tme numercal weather forecast system. Its prmary purpose s to mprove tornado and severe weather warnngs and to assst 30 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 10 - NUMBER 4 - YEAR 2012 ISSN:

2 emergency management response to such events[12]. As a case study for demonstratng the need and effectveness of extendng mult objectve analyss to the computer aded engneerng of CIGUS and to mprove the qualty of hgh consequence technology transton decsons assocated wth ther desgn and development, IP1, has the unque advantage of beng ntensvely and extensvely reported n publc documents and the open lterature[12]. The present study thus provdes a foundaton for extendng computer engneerng ads to support and evaluate techncal readness decsons to cases where such nformaton s not so readly avalable (e.g. SBInet[14]). The desgn of complex sensor systems, such as weather radars and weather radar networks, was accomplshed over years of exploraton and teraton[15], [16] by multple uncoordnated efforts. Whle ths tradtonal process, whch nvolves both tral and error and systematc desgn, has provded the sensor communty wth a new means of weather sensng and predcton[12], t cannot solve the present communcaton problem. One lmtaton of ths approach s that t only allows for a temporary soluton to a partcular systems engneerng problem that wll need to be revsted as future requrements are ntroduced case by case. Here we present for the frst tme, the Pareto optmal mult-objectve analyss of CIGUS. As we dscuss elsewhere[17] ths enables us to capture the evoluton of a partcular speces of CIGUS over many generatons. Varous benefts such as: evolutonary context, reuse, accelerate development, and reduced rsk. Whle the prmary and essental qualty that s demanded of CIGUS s nformatveness, unnformatveness provdes the prncpled way to construct qualty loss functons. The theory underlyng the present formulaton s developed elsewhere[17], n ths paper we present the salence of a specfc applcaton. Informaton produced by such systems s unnformatve to the extent that t s already known, that s to say the pror or to the extent that t s uncertan. Up to now, genetc and evolutonary algorthms have offered or developed nether effectve nor prncpled approaches to ncorporatng such prors and uncertanty. (Un)nformatveness s key and well suted to the engneerng of such adaptve ntellgence orented systems and systems of systems because t s drectly related to the prncple of maxmum entropy[18] as poneered by Jaynes[19] and subsequently developed[20], makng the form of the engneerng problem presented here ntellgble n a way that enables the applcaton of mult-objectve evolutonary algorthms. Weather radar networks are partcularly suted to our nnovatve approach because, although mplct, maxmum entropy prncple s embedded n the core sgnal processng formulaton[21]. (Un)Informatveness provdes a natural level of abstracton whch fully respects and consstently subsumes lower levels such as those assocated wth tradtonal approaches to sensng, sgnalng and communcaton [9], [22], [23]. In ths paper, we make use of the connecton between maxmum entropy and Shannon nformaton theory to cast objectve functons n terms famlar to the engneerng communty. Ths has the added beneft of separatng the concerns of channel provder and content provder. As shown n fgure 1, sets of nformaton orented measures of the performance of sensor systems may be represented n components of an overall objectve vector for purposes of evaluaton and optmzaton. Work completed n [17] show how these measures abstract the sensor system estmators of the underlyng parameters of the overall system n terms of vrtual sensors. By extractng the relevant nformaton from the underlyng parametrc sgnal models, expressed n terms of the language of the subdoman, experts enable a reduced set of nformaton metrcs that are most relevant to CIGUS. The complexty of the sensor networks consdered here results n vectors wth hgh dmensons that make t dffcult for the decson Fg. 1: The nformatve measures are abstracton over the sensor system estmators and parameters allowng ntegraton over, and characterzaton of, a sngle or network of sensors. Objectve functons formulated wth nformatve measures capture the mpact of varyng parameters, desgn vector, on systems and networks of systems. makers to comprehend. Here we explore the effectveness of usng mult-objectve genetc algorthms(moga) n concert wth recent vsualzaton advances for computer aded engneerng to facltate the decson makng process that goes nto the evoluton of complex nformaton gatherng and utlzng systems, such as weather radar networks and partcularly prospectve adaptve networks. A. Informaton Orented Objectve Functons for Atmospherc Sensors Informaton based objectve functons enable channelzaton sensor nformaton flows n accordance wth the value and mpact of the nformaton. A vrtual sensor s comprsed of an element, called a test charge, that nteracts wth the envronment that provdes a measure of the stmulus, an element that receves the sgnal correspondng to ths measure and a medatng element. In general, a phenomenologcal feld, such as the weather, s sampled by sets of vrtual sensors, each correspondng to a dfferent measure and havng ts own characterstc channel. The nformaton orented measures are bult on the prncples of maxmum entropy and the concept of adaptve channel models that capture the scenes multple spatal and temporal dstrbutons. Adaptve channels model the nteracton between the radar and test pattern, ncludng propagaton effects. The measures can be aggregated and stored n a data structure that consoldates all collaboratve vewponts on a common grd of vectors, contanng all the utlzable nformaton gathered from the scene[17]. The sensors may be mxed or fused at the channel level of abstracton enablng desgn and ntensve optmzaton of dverse sensor networks. A partcular dstrbuton of the phenomenologcal feld salence and sensng nstrumentaton s modeled by a test pattern whch represents a scenaro from a set of vewponts n support of requrements engneerng Scannng of test patterns by the smulated sensng system n space and tme can be modeled as a graph traversal problem wth the nodes representng subspaces to be sampled and the arcs weghed by the tme cost. Each subspace, node on the graph, s a regon defned by the beam sold angle, θ s φ s, and range extent, R s. The objectve functons used n the present work are chosen to explore the trade-offs between the conflctng objectves of nformaton capacty, gathered nformaton, qualty of nformaton, cost, and scan tme. The objectve functons, J (θ), where the subscrpt s the th objectve functon, and θ s the desgn vector, are constructed for a typcal weather scene as follows: J 1(θ) = `Is rcap + Iv cap s (1) ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 10 - NUMBER 4 - YEAR

3 J 6(θ) = J 2(θ) = J 3(θ) = J 4(θ) = J 5(θ) = Ir HDs cap (2) (Ir s ) (3) (Iv) s (4) I HDs r SP s `BER r + BER sˆv r + BER sˆσ vr J 7(θ) = 3S (5) (6) S 1 X s `T subspace + (Ttrans) s (7) J 8(θ) = cost Rbase + cost power + cost aglty + cost antenna (8) There are two classes of targets, sx weather subspaces and sx hard target subspaces. The nformaton orented measures of nformaton capacty (Ir s cap and Iv s cap ), nformaton (Ir s and Iv), s and Bt Error Rate (BERr, s BER sˆv r, and BER sˆσ vr ) are captured n equatons (1)- (6). The superscrpt HD ndcates hard target nformaton orented measures and the subscrpt s s used to dentfy the s th subspace. The frst two objectve functons, (1) and (2), sum the nformaton channel capacty for weather and hard targets over the subspaces, respectvely. Three types of nformaton capacty, reflectvty(i rcap ), velocty(i vcap ), and hard target(ir HD cap ), are defned nstantaneously as the maxmum bt rate that can be sustaned by channel models of a gaussan whte nose channel, and noseless gaussan channel, and a Swerlng 1 model channel, respectvely[17]. The hard target velocty capacty s not calculated. In the present analyss the objectve functons of channel capacty are mnmzed to ensure maxmum capacty utlzaton. Objectve functons J 3, J 4, and J 4 are comprsed of the aggregated nformaton gathered over the ndvdual reflectvty, velocty, and hard target reflectvty channels, whch are then summed over the subspaces, respectvely. Hard target velocty nformaton s not calculated. These functons are maxmzed. The bt error rates are a measure of the qualty of the nformaton extracted and are a functon of the errors n the underlyng estmators. Objectve functon J 6 used n ths analyss consoldated the BER assocated wth the varous channels to provde an overall qualty of nformaton measure. The summaton s over S, the subspaces, of the ndvdual terms of each subspace referrng to the reflectvty, (BER r) the velocty (BERˆvr ), and the spectrum wdth (BERˆσvr ). Hard target reflectvty or velocty bt error rate s not calculated. Mnmzng the BER, maxmzes accuracy and precson of the nformaton[17]. Objectve functon J 7 s a measure of the total tme t takes to acqure the nformaton n the scene. It s a measure of the nformaton gatherng throughput of the system, the amount of nformaton collected for the tme to complete the test pattern scan. The tme objectve functon s splt nto two summaton, the frst s the tme to scan each subspace, the second s the tme taken to scan between each subspace. The tme to scan each subspace, Tsubspace, s s gven by the dwell tme of the radar, DT, and the number of postons n azmuth, B az = θs, and elevaton, B θ el az3 = φs db φ el3, necessary to db scan the entre subspace and the tme to transton from beam to beam wthn the subspace. The tme to move from subspace to subspace, Ttrans, s s gven by rotatng the sensor. Equatons (9) and (10) defne the subspace tme and transton tme. T s subspace = B azb el DT + B el [(B az 1)az tb2b] + (B el 1)el tb2b (9) T s subspace = az s ts2s + el s ts2s (10) where az tb2b, and el tb2bare the tmes to transton from beam poston to beam poston. In the case of the transton from subspace to subspace, az ts2s and el ts2s, the tme s gven by the angular dfference n azmuth and elevaton multpled by the angular velocty n that drecton. Mnmzng J 7, maxmzes the throughput. Objectve functon J 8 s a measure of the cost of the system. The cost objectve functon, J 8(θ), s made up of four factors; base radar cost, excess power cost, excess aglty cost, and excess antenna cost. Our ntal objectve cost functon s a frst approxmaton to the true cost functon to be created and s referenced to the cost values for the IP1 weather radars[24], [12]. Cost s mnmzed. In ths study we chose the followng decson varables: maxmum transmt power, half power beam wdth n azmuth and elevaton, and maxmum angular velocty of the pedestal, gven n table I to make up the decson vector, θ = [θ 1, θ 2, θ 3, θ 4]. These varables were chosen because the object functons are most senstve to them and are suffcent for valdatng the approach. In the present case of computer aded engneerng of a sngle radar we have reduced our objectve vector, J(θ), to eght dmensons, correspondng to the sx aspects of the scene about whch we seek to gather nformaton, the tme nterval over whch we seek t, and the cost of the deployed system. B. Mult-Objectve Genetc Algorthms Mult-objectve optmzaton seeks to optmze problems that requre the smultaneous optmzaton of multple, often competng objectves [3]. Genetc Algorthms were orgnally developed to mtate the process by whch lvng organsms evolve [4]. They have snce been appled to mult-objectve optmzaton problems as algorthms to supply reasonable approxmatons to the Pareto front and set [25]. Here they are used n a computer aded engneerng approach to smulate the evoluton of complex engneered systems. The techncal analyss supports the decson makers n makng a selecton of a partcular desgn out of the set of Pareto optmal desgns. Each of the solutons returned by the analyss, see Fgure 2, s a vald optmal desgn resultng from tradeoffs among the conflctng objectves reachng mutually non-domnated solutons referred to as the Pareto front. The dscrete set of optmum ponts can then be used by the varous decson makers to drve the evoluton of the complex system beng optmzed, n ths case a cyber-physcal nformaton gatherng and utlzng system. The use of genetcal algorthms to calculate the Pareto front and set of a mult-objectve optmzaton problem s referred to as MOGA. Wthn the present approach we wll demonstrate how MOGA can be used to calculate the Pareto front and set for low order models of a sngle weather radar. Hgher order models can be ncorporated nto MOGA through the use of a more sophstcated smulaton[17]. 32 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 10 - NUMBER 4 - YEAR 2012 ISSN:

4 TABLE I: MOGA Settngs Decson Varables Parameter (Unt) lower ntal upper θ 1 Peak Power (W) 5e3 12.5e3 20e3 θ 2 θ az3db (deg) θ 3 θ el3db (deg) θ 4 Aglty (deg/sec) Cost Varables Value R base $220e3 λ γ 1 2 κ 1 8e3 λ γ κ 2 20 λ γ κ 3 4 For these hgher dmensonal mult-objectve problems, the present approach s an 8 dmenson problem, a vsualzaton technque called Level Dagrams[5] wll be used to enable an mproved analyss of the Pareto front and wll provde an excellent tool for the decson makers. The Level Dagrams classfy each Pareto front by the dstance of the Pareto front from the deal pont, accountng for all the objectves smultaneously. It s extremely unlkely for an optmzed soluton to the Pareto front to acheve the deal pont[6], but we defne the Pareto optmal pont as the pont wth the shortest 1-norm dstance from the deal pont. Every objectve (J (θ), = 1,..., m) s normalzed and classfed wth respect to ts mnmum and maxmum values on the Pareto front, J norm (θ), = 1,..., m [5]: J max such that, = max J (θ), J θ Θ mn = mn J (θ), = 1,..., m (11) θ θ P P J norm (θ) = J(θ) J mn J max J mn (12) 0 J norm (θ) 1 (13) The Y-axs on all the Level Dagram graphs, fgure 2, corresponds to the value of the normalzed objectve functon, and ths means that all graphs are synchronzed wth respect to ths axs. The X- axs corresponds to values of the objectve, or decson varables, n physcal unts. Usng ths representaton, all plots are synchronzed wth respect to the y-axs, meanng a sngle level on the y-axs returns all the nformaton for a sngle pont on any of the objectve functon or decson varables plots[5]. A. Scannng Analyss III. MOGA ANALYSIS: CASE STUDY The MOGA analyss s done wth an agle mechancal pedestal usng the decson varables and cost varables lsted n table I. The Level Dagrams of the Pareto front and set for the MOGA analyss of the agle mechancal X-band radar s gven n fgure 2. The Pareto optmal pont s the lght green square referenced by the arrow. Black vertcal lnes n plots of J 7, J 8, θ 1, θ 2 and θ 3 represent the specfcatons gven n [24], [26] for the IP1 weather radars. Gven the complexty of the mult-objectve problem, t s surprsng to see the Pareto optmal pont comng n close comparson to the documented values of the IP1 weather sensng radar. The Pareto optmal pont returns θ az3db = 1.6 o, θ el3db = 1.9 o, P t = TABLE II: MOGA Analyss Summary Power (P t) θ az3db θ el3db Scan Tme Cost (W) (deg) (deg) (sec) (k$) Smulated IP kW, cost = $459k and tme = 53sec, compared to the IP1 values of θ az3db = 1.8 o, θ el3db = 1.8 o, P t = 8kW, cost = $459k and heart beat tme = 60sec. IV. DISCUSSION The present computer aded engneered approach appled to the gven weather radar sensor results n a well formed hgh dmenson Pareto front yeldng the Pareto optmal pont close to the deal pont. The 1-norm Level Dagrams, shown n fgure 2, have smooth objectves wth well defned mnma where no sngle objectve domnates, suggestng convexty of the Pareto front. Combned wth locaton of the 1-norm Pareto optmal pont to wthn 25% of the deal pont, we can characterze the Pareto front as well formed. Therefore, the Level Dagrams are provdng nsght nto hgh dmenson Pareto fronts when based on nformaton orented measures and test patterns. The resultng Pareto optmal desgn vector yelded values, on average, n excellent correspondence wth the actual IP1 desgn. An agreement between the optmal desgn vector and IP1 desgn of wthn 10% for the scan tme s evdence that the current test pattern s a good representaton of a multtask scene. Further ndcaton s the smlarty, wthn 10%, of the optmal azmuth and elevaton beam wdth to the IP1 desgn. The Pareto optmal peak transmt power, a relatvely outler at 18% greater than the IP1 desgn, s a result of the magnetron transmtter n the IP1 radar operatng below ts maxmum rated peak power. The present computer aded engneered approach accurately models the evoluton of IP1 system. Although the results exhbt excellent convergence, extendng the objectve vector to nclude a relablty/avalablty component would lkely result n further convergence between the Pareto desgn and real case. However, a vald and verfed relablty/avalablty model for the present case under study has not appeared n the lterature. As the models become avalable, they can be ncorporated nto the mult-objectve optmzaton adng n the engneerng of the system. The computer aded engneerng approach provdes solaton from the other objectve functons allowng hgher level models for cost, relablty, mantanablty, volume manufacturng, ndustral learnng curves, and other potental non-functonal and functonal requrements to be readly ncorporated or modfed. MOGA smultaneously evaluates each of the objectve functon ndvdually. Ths allows the objectve functons to be ndvdually modfed wthout the need to update subjectve weghts. The addtonal abstracton of the nformatve objectve functons allows the ncluson of uncertanty and prors nto the MOGA analyss and encourages the use of other mult-objectve evolutonary algorthms(moea) that may be better for other applcatons. The method presents an approach allowng for the acceleraton of the evoluton of complex, mult-crteron nformaton gatherng and utlzng systems. Extenson to hgher order models of sgnal estmators and test patterns n the presence of multple weather sensors s of nterest to provde nsght nto desgn trades over changng weather condtons and dfferent venues. Specfcally, creaton of hgher order models of the sensor system and test pattern wll facltate exploraton nto the trade space of polarmetrc weather radar networks and waveform desgn for network multfuncton radars. Moreover, the ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 10 - NUMBER 4 - YEAR

5 Fg. 2: 1-norm Level Dagram of the Pareto front and set the eght objectve functons comprsng the objectve vector, J (θ), where the subscrpt s the th objectve functon, and θ s the desgn vector used n the MOGA analyss of the case study X-band weather radar descrbed n secton III-A. The Pareto optmal pont s the lght green square referenced by the arrow. Black vertcal lnes n plots of J 7, J 8, θ 1, θ 2 and θ 3 represent the specfcatons gven n [24], [26] for the IP1 weather radars. method can be extended to ncorporate further decson support for more complex trade-off analyss that may be requred to assess the evoluton at hgher levels to support busness modelng and plannng. V. CONCLUSION We have shown that by ntroducng ntegratve objectve nformaton orented measures, we can defne a level of abstracton whch captures the underlyng sensor estmators and parameters that solves the communcaton problem between the systems engneers, doman experts and decson makers. Not only wll the obstacle be elmnated, the desgn of these complex sensor systems wll converge much more rapdly, allowng for an acceleraton n the evoluton of the systems, wth the ncluson of the preferences of decson makers a posteror to the objectve analyss, hence acknowledgng subjectve nfluences. The analyss s appled to weather radar desgns provdng complex mult-objectve desgn problems wth evolvng specfcatons and requrements. Wthout any adjustable parameters, any subjectve weghtng, and n such a complex desgn space where a multplcty of results could have occurred, the nformatve methodology of systems engneerng resulted n decson parameters very close to that of the IP1 system. The results of the MOGA analyss case study, show that the approach s successful n modelng the complex system by producng a Pareto optmal pont wthn an average of 10% of the case study s desgn specfcatons and provdng an objectve bass for evaluatng the engneerng feasblty of the end-to-end system and ts transton nto operatonal envronments for further development. The foregong capabltes facltate the demonstraton of engneerng feasblty and subsequent development and evoluton of the CIGUS. We develop objectve functons, combnng measures of cost and throughput wth the underlyng doman specfc parameters, enablng the applcaton of state-of-the-art mult-objectve evolutonary algorthms and automated decson support tools. The novel systems engneerng approach s further valdated and verfed by the agreement of the predctons of the analyss and the expermental data from the IP1 test bed. Clearly, n the case of weather radars had the present approach been avalable, consderable tme and money could have been saved[17]. REFERENCES [1] Z. Song, Y. Chen, C. R. Sastry, and N. C. Tas, Optmal Observaton for Cyber-physcal Systems: A Fsher-nformaton-matrx-based Approach, 1st ed. Sprnger, Aug [2] J. M. Carlson and J. Doyle, Hghly Optmzed Tolerance: Robustness and Desgn n Complex Systems, Physcal Revew Letters, vol. 84, no. 11, pp , Mar [Onlne]. Avalable: http: //dx.do.org/ /physrevlett SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 10 - NUMBER 4 - YEAR 2012 ISSN:

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