本文選題：多個(gè)體系統(tǒng) + 能控性　； 參考：《南京師范大學(xué)》2017年碩士論文

【摘要】：多個(gè)體系統(tǒng)是具有一定網(wǎng)絡(luò)結(jié)構(gòu)的一組動(dòng)態(tài)系統(tǒng).從數(shù)學(xué)模型上來看,多個(gè)體系統(tǒng)就是一組具有圖結(jié)構(gòu)的微分方程組或者差分方程組.多個(gè)體系統(tǒng)控制理論有廣泛的應(yīng)用背景,比如機(jī)器人群的協(xié)作,無人機(jī)群的編隊(duì)以及衛(wèi)星群的姿態(tài)同步.多個(gè)體系統(tǒng)控制理論擴(kuò)展了傳統(tǒng)單個(gè)體系統(tǒng)的控制理論,是結(jié)合了圖論、微分方程理論和控制理論的一個(gè)新的研究分支.多個(gè)體系統(tǒng)的牽引控制就是通過控制動(dòng)態(tài)網(wǎng)絡(luò)中的某些節(jié)點(diǎn)來控制整個(gè)系統(tǒng)的行為.能控性是動(dòng)態(tài)系統(tǒng)控制理論中的一個(gè)基本概念,它反映了外部輸入對系統(tǒng)行為的控制能力.多個(gè)體系統(tǒng)在牽引控制下的能控性則是探究能否通過牽制部分節(jié)點(diǎn)來實(shí)現(xiàn)對整個(gè)動(dòng)態(tài)網(wǎng)絡(luò)的控制能力,它正在逐步發(fā)展成為一個(gè)新的研究熱點(diǎn).本文主要研究了線性多個(gè)體控制系統(tǒng)在牽引控制下的能控性問題.首先建立了一個(gè)一般形式的數(shù)學(xué)模型,該模型涵蓋了已有文獻(xiàn)中的模型,并將已有的結(jié)果推廣到了這個(gè)一般化模型中,得到了能控性的必要條件以及充分條件.其次針對一些具體的網(wǎng)絡(luò)結(jié)構(gòu)包括圈圖、完全圖、星狀圖及Petersen圖,給出了牽引控制的設(shè)計(jì),并對能控性給出了證明.
[Abstract]:Multi-individual system is a group of dynamic systems with a certain network structure. From the mathematical model, the multi-individual system is a group of differential equations or difference equations with graph structure. The theory of multi-individual system control has a wide application background, such as the cooperation of robot crowd, the formation of UAV and the attitude synchronization of satellite group. The control theory of multi-individual systems extends the control theory of traditional single-individual systems and is a new branch of research which combines graph theory differential equation theory and control theory. The traction control of multi-individual system controls the behavior of the whole system by controlling some nodes in the dynamic network. Controllability is a basic concept in dynamic system control theory, which reflects the ability of external input to control system behavior. The controllability of multi-individual system under traction control is to explore whether the control ability of the whole dynamic network can be realized by restraining some nodes, and it is gradually developing into a new research hotspot. In this paper, the controllability of linear multi-individual control system under traction control is studied. Firstly, a general mathematical model is established, which covers the existing models in the literature, and extends the existing results to the generalized model. The necessary conditions and sufficient conditions for controllability are obtained. Secondly, the design of traction control is given and the controllability is proved for some specific network structure including cycle graph, complete graph, star graph and Petersen diagram.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O231

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 劉波;史運(yùn)濤;蘇厚勝;韓瀟;;Second-Order Controllability of Multi-Agent Systems with Multiple Leaders[J];Communications in Theoretical Physics;2016年05期

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本文編號：1861925