復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)簡(jiǎn)介

復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)簡(jiǎn)介陳關(guān)榮(GuanrongChen)香港城市大學(xué)電子工程系講座教授、IEEEFellow混沌與復(fù)雜網(wǎng)絡(luò)學(xué)術(shù)研究中心主任gchen@.hk摘要復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)涉及到物理、數(shù)學(xué)、工程、生物、甚至經(jīng)濟(jì)和社會(huì)科學(xué)，其影響廣泛而深遠(yuǎn)。典型的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)包括Internet、WWW、HTTP、無(wú)線電通信網(wǎng)、生物大腦神經(jīng)網(wǎng)、社會(huì)政治和經(jīng)濟(jì)網(wǎng)、以及科研合作關(guān)系網(wǎng)，等等。關(guān)于復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的基本理論及其應(yīng)用的研究最近非常熱鬧，正在不同的學(xué)科和領(lǐng)域里廣泛開(kāi)展。這個(gè)報(bào)告將簡(jiǎn)單介紹復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的一些基本概念，如平均路徑長(zhǎng)度、類(lèi)聚系數(shù)、節(jié)點(diǎn)度及其分布等，特別是將介紹經(jīng)典的隨機(jī)圖論和新近發(fā)展起來(lái)的小世界和無(wú)尺度網(wǎng)絡(luò)模型，并以Internet、WWW和科研合作為例解釋這些概念和模型。這個(gè)綜述報(bào)告從最簡(jiǎn)單的常識(shí)講起，并不假定聽(tīng)眾有任何的網(wǎng)絡(luò)知識(shí)背景。演講人簡(jiǎn)介陳關(guān)榮教授于1981在國(guó)內(nèi)獲中山大學(xué)計(jì)算數(shù)學(xué)碩士學(xué)位，1987年獲美國(guó)TexasA&M大學(xué)應(yīng)用數(shù)學(xué)博士學(xué)位，后在Houston大學(xué)任教、為終身職正教授。2000年起接受香港城市大學(xué)邀請(qǐng)任講座教授，創(chuàng)立了《混沌與網(wǎng)絡(luò)學(xué)術(shù)研究中心》并任主任。陳關(guān)榮教授畢業(yè)后一直在工程學(xué)院工作，從事非線性科學(xué)研究，是IEEEFellow，IEEE電路與系統(tǒng)-I常務(wù)主編及國(guó)際分岔與混沌等多個(gè)國(guó)際雜志的編輯或編委。他曾經(jīng)擔(dān)任許多國(guó)際會(huì)議和論壇的主席和組織者及程序技術(shù)委員會(huì)委員,曾任IEEE電路與系統(tǒng)學(xué)會(huì)非線性電路與系統(tǒng)技術(shù)委員會(huì)主席。目前發(fā)表國(guó)際雜志論文400多篇、會(huì)議論文200多篇、出版專(zhuān)著和高等教材16部。陳關(guān)榮教授是國(guó)內(nèi)十多所大學(xué)的榮譽(yù)客座教授，并多次應(yīng)邀到30多個(gè)國(guó)家講學(xué)。復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的合作控制CooperativeControlofComplexDynamicNetworks

問(wèn)題描述ProblemDescription在過(guò)去的二十年中，網(wǎng)絡(luò)和分布式計(jì)算的迅猛發(fā)展造就了從大型集成電路計(jì)算機(jī)到分布式網(wǎng)絡(luò)工作站的一個(gè)躍變。在工業(yè)應(yīng)用中，我們期望能夠應(yīng)用許多價(jià)格低廉的小型設(shè)備之間的相互協(xié)調(diào)合作來(lái)替代原來(lái)造價(jià)昂貴，設(shè)計(jì)復(fù)雜的大型集成電路設(shè)備。多智能體網(wǎng)絡(luò)的分布式協(xié)調(diào)合作控制問(wèn)題近年來(lái)引起了越來(lái)越多學(xué)者的關(guān)注，這主要?dú)w因于多智能體系統(tǒng)在各行各業(yè)的廣泛應(yīng)用，這其中包括無(wú)人駕駛飛行器的合作控制(UAVS),形成控制(formationcontrol),flocking,群集(swarming),分布式傳感器網(wǎng)絡(luò)(distributedsensornetworks)，衛(wèi)星的姿態(tài)控制(attitudealignmentofclustersofsatellites),以及通訊網(wǎng)絡(luò)當(dāng)中的擁塞控制(congestioncontrol).

典型例子TypicalExamples

Flocking在一個(gè)多智能體系統(tǒng)中，所有的智能體最終能夠達(dá)到速度矢量相等，相互間的距離穩(wěn)定，我們稱(chēng)為Flocking問(wèn)題。Flocking算法最早是由Reynolds在1986年提出。當(dāng)時(shí)為了在計(jì)算中模擬Flocking，他提出了三條基本法則:(1)separation;(2)cohesion;(3)alignment。Vicsek于1995年提出并研究了Reynolds模型的一個(gè)簡(jiǎn)化模型。在它的模型中，所有的主體保持相同的速度運(yùn)行，這個(gè)僅僅體現(xiàn)了Reynolds算法中的alignment。近年來(lái)，許多控制學(xué)者也在研究Flocking問(wèn)題，他們通過(guò)構(gòu)建微分方程組將Flocking問(wèn)題進(jìn)行抽象化，利用人工勢(shì)能結(jié)合速度一致(consensus)的方法來(lái)實(shí)現(xiàn)Flocking算法。

Swarming群集(swarm)是一個(gè)由大量自治個(gè)體組成的集合，在無(wú)集中式控制和全局模型的情況下，一般通過(guò)個(gè)體的局部感知作用和相應(yīng)的反應(yīng)行為，使整體呈現(xiàn)出涌現(xiàn)行為。群集具有個(gè)體自治、非集中式(decentralized)控制、局部信息作用(localinteraction)等特征。在自然界中，群集無(wú)處不在，在幾乎所有的尺度上，從非生命世界的分子到星系，從生物界的簡(jiǎn)單的細(xì)菌到高等動(dòng)物，普遍存在著群集現(xiàn)象和群集行為。研究群集系統(tǒng)具有實(shí)際意義，它是理解生物復(fù)雜性的一個(gè)途徑，一方面，可以借鑒生物的智慧，把分布式策略用在自治多代理系統(tǒng)（如多機(jī)器人或自治飛行器系統(tǒng)）的控制、協(xié)調(diào)以及編隊(duì)控制中。這些系統(tǒng)的共同特點(diǎn)是：無(wú)集中式控制、無(wú)全局通訊、個(gè)體自治。通過(guò)設(shè)計(jì)一定的控制律，可以使系統(tǒng)整體呈現(xiàn)出所期望的涌現(xiàn)行為。另一方面，群集有可能來(lái)解釋群集智能(swarmingintelligence)的產(chǎn)生，每一個(gè)個(gè)體并不是非常智慧的主體，但它們之間通過(guò)協(xié)作卻可以展現(xiàn)出一定的智能行為。群集是一個(gè)分布式協(xié)作系統(tǒng)，具有魯棒性和自組織的特征，群集系統(tǒng)是基于局部?jī)?yōu)化的系統(tǒng)，在效率和魯棒性方面可能要比傳統(tǒng)的集中式控制更有優(yōu)勢(shì)，因而具有工程上潛在的應(yīng)用價(jià)值，特別是大尺度上的行為對(duì)局部失效和故障不敏感，這是集中式控制所沒(méi)有的特征。

Consensus(Agreement)在一個(gè)多智能體系統(tǒng)中，所有的智能體最終狀態(tài)能夠趨于一致，我們稱(chēng)為一致性問(wèn)題。一致性問(wèn)題的出現(xiàn)主要源于合作控制問(wèn)題.對(duì)于多智能體系統(tǒng)的合作控制問(wèn)題,智能體之間共享信息是保證合作的一個(gè)前提條件,共享信息可以以多種形式出現(xiàn),比如說(shuō)一個(gè)共同的目標(biāo),一種共同的控制算法,相對(duì)的位置信息,或者是一張世界地圖.當(dāng)一組智能體要合作共同去完成一項(xiàng)任務(wù),合作控制策略的有效性表現(xiàn)在,多智能體必須能夠應(yīng)對(duì)各種不可預(yù)知的形勢(shì)和環(huán)境的改變,這就要求智能體隨著環(huán)境的改變能夠達(dá)到一致.因此,多智能體達(dá)到一致是實(shí)現(xiàn)協(xié)調(diào)合作控制的一個(gè)首要條件.

Rendezvous一群移動(dòng)的智能體最后能夠在某一點(diǎn)聚集，我們稱(chēng)為聚集問(wèn)題。聚集問(wèn)題的發(fā)展源于機(jī)器人應(yīng)用的發(fā)展，比如說(shuō)，一群機(jī)器人要合作完成一個(gè)任務(wù)，到達(dá)一個(gè)共同的地點(diǎn)，在一片未知的地方進(jìn)行搜救工作，或者一群無(wú)人駕駛飛機(jī)要達(dá)到一個(gè)共同地點(diǎn)等。

參考文獻(xiàn)References

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Rendezvous[1].

JorgeCortes,SoniaMartinez,FrancescoBullo,Robustrendezvousformobileautonomousagentsviaproximitygraphsinarbitrarydimensions,IEEETrans.onAutomaticControl,2005,13:200-208.[2].

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