本文選題：魯里葉系統(tǒng)　切入點(diǎn)：非線性網(wǎng)絡(luò)　出處：《哈爾濱工業(yè)大學(xué)》2015年博士論文　論文類型：學(xué)位論文

【摘要】：由多個(gè)單系統(tǒng)(又稱為智能體)以相互協(xié)作的方式組成的大規(guī)模網(wǎng)絡(luò)化系統(tǒng)具有功能強(qiáng)大、靈活度高、成本低廉等優(yōu)勢(shì),是編隊(duì)航天器系統(tǒng)、多機(jī)器人系統(tǒng)、智能電網(wǎng)等工程問(wèn)題的通用化理論模型。為實(shí)現(xiàn)網(wǎng)絡(luò)化系統(tǒng)的協(xié)同工作,需要對(duì)網(wǎng)絡(luò)中的各個(gè)成員進(jìn)行分布式控制,以協(xié)同完成預(yù)定的目標(biāo)任務(wù)。分布式控制的核心是,僅利用網(wǎng)絡(luò)中相鄰智能體間的(局部)相對(duì)信息,將動(dòng)態(tài)網(wǎng)絡(luò)的群體行為協(xié)調(diào)到期望的狀態(tài),如達(dá)到同步。對(duì)諸如考慮執(zhí)行機(jī)構(gòu)含有飽和或死區(qū)等區(qū)間非線性的航天器動(dòng)力學(xué),可以由魯里葉系統(tǒng)來(lái)描述。因此,本論文針對(duì)節(jié)點(diǎn)動(dòng)力學(xué)為魯里葉系統(tǒng)的非線性多智能體網(wǎng)絡(luò),基于代數(shù)圖論、絕對(duì)穩(wěn)定性理論、線性矩陣不等式、魯棒H∞/最優(yōu)等控制技術(shù),開(kāi)展該類網(wǎng)絡(luò)化系統(tǒng)的魯棒同步問(wèn)題研究,取得如下研究成果:針對(duì)能夠由連通無(wú)向圖表示的無(wú)領(lǐng)航者多魯里葉系統(tǒng),考慮經(jīng)靜態(tài)相對(duì)狀態(tài)反饋分散耦合而成的動(dòng)態(tài)網(wǎng)絡(luò)魯棒同步問(wèn)題,提出了分別考慮增量無(wú)源魯里葉非線性與增量扇區(qū)有界魯里葉非線性下的完全分布式魯棒同步算法。理論證明給出如下結(jié)論:任意連通無(wú)向圖的拉普拉斯矩陣的非零特征根對(duì)應(yīng)的特征向量張成的矩陣與其自身轉(zhuǎn)置的乘積生成的矩陣為節(jié)點(diǎn)數(shù)相同的無(wú)權(quán)完全圖的拉普拉斯矩陣。利用該結(jié)論構(gòu)造無(wú)向魯里葉網(wǎng)絡(luò)的同步誤差系統(tǒng),分析該誤差系統(tǒng)全局漸近穩(wěn)定的充分條件,給出了靜態(tài)相對(duì)狀態(tài)反饋同步協(xié)議中反饋增益矩陣的設(shè)計(jì)方法。進(jìn)一步,在上述靜態(tài)相對(duì)狀態(tài)反饋同步協(xié)議中引入自適應(yīng)耦合權(quán)重,實(shí)現(xiàn)由局部同步誤差驅(qū)動(dòng)的各邊權(quán)重的動(dòng)態(tài)調(diào)整,理論分析證明,該時(shí)變權(quán)重的引入能夠在無(wú)不知道完整網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)的情況下實(shí)現(xiàn)無(wú)向魯里葉網(wǎng)絡(luò)的魯棒同步。進(jìn)一步針對(duì)強(qiáng)連通有向圖的情況,設(shè)計(jì)了一種有向魯里葉網(wǎng)絡(luò)的魯棒同步算法�；趶�(qiáng)連通有向圖的拉普拉斯矩陣對(duì)應(yīng)零特征根的左特征向量,構(gòu)造了同步誤差系統(tǒng)及相應(yīng)的李雅普諾夫函數(shù),并利用強(qiáng)連通有向圖的廣義代數(shù)連通度證明了該誤差系統(tǒng)的全局漸近穩(wěn)定性,從而證明了所設(shè)計(jì)的同步算法是有效的。由于含有一條有向生成樹(shù)的有向圖總能劃分成多個(gè)強(qiáng)連通子圖,能夠利用強(qiáng)連通圖的相關(guān)結(jié)論給出由該有向圖中所有根節(jié)點(diǎn)組成的強(qiáng)連通子圖上的多魯里葉系統(tǒng)同步的充分條件,再理論證明該有向圖中其余節(jié)點(diǎn)上的魯里葉系統(tǒng)可收斂于根節(jié)點(diǎn)的同步流型,從而給出含有一條有向生成樹(shù)的有向魯里葉網(wǎng)絡(luò)的魯棒同步算法。針對(duì)僅有相對(duì)測(cè)量輸出信息可用的無(wú)向魯里葉網(wǎng)絡(luò)的魯棒同步問(wèn)題,考慮魯里葉非線性未知的情況,提出了一種基于相對(duì)測(cè)量輸出線性動(dòng)態(tài)反饋同步協(xié)議的設(shè)計(jì)方法。在構(gòu)造同步誤差系統(tǒng)并分析其全局漸近穩(wěn)定性的基礎(chǔ)上,證明了同步協(xié)議參數(shù)矩陣需要滿足的充分條件,進(jìn)一步基于線性H∞控制技術(shù),給出了這些參數(shù)矩陣的計(jì)算方法。由于我們所設(shè)計(jì)的同步協(xié)議是動(dòng)態(tài)的,對(duì)其狀態(tài)空間維數(shù)的選取也一并做了討論。由于未對(duì)魯里葉非線性作精確已知的假設(shè),只需滿足增量無(wú)源或增量扇區(qū)有界條件,我們所設(shè)計(jì)的同步協(xié)議在這個(gè)意義下是魯棒的。由于實(shí)際網(wǎng)絡(luò)化系統(tǒng),如智能電網(wǎng)等中的節(jié)點(diǎn)動(dòng)力學(xué)并不完全一致,為此假設(shè)所有魯里葉系統(tǒng)的線性部分是一致的,而其非線性部分可以是不同的,引入輸出調(diào)節(jié)理論,分別提出了基于動(dòng)態(tài)狀態(tài)反饋與動(dòng)態(tài)輸出反饋的異構(gòu)魯里葉網(wǎng)絡(luò)的魯棒輸出同步協(xié)議設(shè)計(jì)方法。該方法采用分布式觀測(cè)器技術(shù),首先在含有一條有向生成樹(shù)的有向網(wǎng)絡(luò)上設(shè)計(jì)一個(gè)同構(gòu)分布式觀測(cè)器網(wǎng)絡(luò),在每個(gè)節(jié)點(diǎn)處漸近地復(fù)現(xiàn)一個(gè)共同的參考信號(hào),然后基于輸入狀態(tài)穩(wěn)定性理論,設(shè)計(jì)局部輸出調(diào)節(jié)控制器現(xiàn)實(shí)各智能體對(duì)該參考信號(hào)的跟蹤控制。由于分布式觀測(cè)器的引入,使得局部輸出調(diào)節(jié)控制器的設(shè)計(jì)不局限于魯里葉系統(tǒng),因此本方法可用于處理任意節(jié)點(diǎn)動(dòng)態(tài)的異構(gòu)網(wǎng)絡(luò)同步問(wèn)題。
[Abstract]:A single system (also called agent) large-scale networked system with mutual cooperation way has strong function, high flexibility, low cost and other advantages, is the formation of spacecraft system, multi robot system, smart grid and other engineering problems. A general theoretical model for collaborative work of network system the need for distributed control of each member of the network, in order to complete the objectives and tasks scheduled. Collaborative distributed control is the core, only the use of adjacent intelligent network between the (local) relative information, the group behavior coordination of dynamic network to the desired state, such as synchronization of Interval Nonlinear Dynamics of spacecraft. Such as considering actuator saturated or dead, by Ruriye to describe the system. Therefore, this thesis focuses on the node dynamics of nonlinear Lurie system of multi agent based network. In algebraic graph theory, the theory of absolute stability, linear matrix inequality, the robust H / optimal control technology, to carry out research on robust synchronization of the network system, the main achievements were as follows: the leader Doru Lee Ye system can be represented by undirected graph, considering the dynamic network robust synchronization problem by static state feedback decentralized coupled together, put forward respectively considering the incremental passive Lurie and incremental nonlinear sector bounded nonlinear Lurie under fully distributed robust synchronization algorithm. Theoretical proof is given as follows: arbitrary undirected non product feature vectors in a matrix with zero eigenvalues and its transpose matrix Laplasse matrix the figure for the same number of nodes to end the Laplasse matrix map. The synchronization error system to Lurie network using this conclusion structure, The error analysis of sufficient conditions for global asymptotic stability of the system, given the relatively static state feedback design method of feedback gain matrix synchronization protocol. Further, the introduction of adaptive weights in the coupled relative static state feedback synchronization protocol, to realize the dynamic adjustment of each edge weights by local synchronization error driven, theoretical analysis shows that the introduction of the when the variable weight can all know the complete network topology under the condition of non synchronization to robust Lurie network. Aiming at the strongly connected directed graph of the situation, has designed a robust synchronization algorithm to the network. Ruriye strongly connected directed left eigenvector matrix of the Laplasse graph corresponding to zero eigenvalue based on the structure of the synchronization error system and the corresponding Lyapunov function, and the use of strong connectivity to generalized algebraic connectivity of a proof of the error system The global asymptotic stability and synchronization algorithm so as to prove the design is effective. Because it contains a directed spanning tree directed graph is always divided into a plurality of strongly connected subgraph, leaf synchronization sufficient condition can by the composition of the root node to the graph all strongly connected subgraph with given conclusion the Shandong strongly connected graph, then it is proved that the synchronization pattern to other nodes on the Ruriye system diagram can converge to the root node, which is containing a directed spanning tree to robust synchronization algorithm of Lurie network. According to the only output information available without relative measurement to the problem of robust synchronization of Lur'e network, considering the nonlinear unknown Rury, presents a design method of measuring the relative output linear dynamic feedback synchronization protocol. Based on structural system and analyses its full synchronization error Based on the asymptotic stability of the Bureau, we establish sufficient conditions for the parameter matrix to satisfy the synchronization protocol, further based on linear H control technology, the calculation method of parameter matrix is given. The synchronization protocol designed by us is dynamic, the selection of the state space dimension are also discussed. Because of not accurate known for Lur'e nonlinear assumptions, only need to meet the incremental passive or incremental sector boundary conditions, we design the synchronization protocol is robust in this sense. Because of the actual network system, such as node dynamics in the smart grid is not exactly the same, so the assumption of linear part of all of the Ruriye system is consistent but, the nonlinear part can be different, the output regulation theory, respectively, proposed a dynamic state feedback and dynamic output feedback Lurie heterogeneous network based on Shandong Best output synchronization protocol design method. This method adopts distributed observer techniques, first in contains a directed spanning tree has designed a homogeneous distributed network to network observer, at each node asymptotically reproducing a common reference signal, then input state stability based on the theory, the design of local controller real output each agent of the reference signal tracking control. Due to the introduction of distributed observer, design the local controller output is not limited to Lurie system, so this method can be used to deal with heterogeneous network synchronization at any node dynamically.

【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：O231.4

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1 張凡;網(wǎng)絡(luò)化魯里葉系統(tǒng)的分布式控制研究[D];哈爾濱工業(yè)大學(xué);2015年

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本文編號(hào)：1597579