本文關鍵詞：一類分數(shù)階多智能體系統(tǒng)的可控性研究　出處：《北方工業(yè)大學》2017年碩士論文　論文類型：學位論文

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【摘要】：分數(shù)階多智能體系統(tǒng)的可控性已經(jīng)成為研究智能體系統(tǒng)的一個熱點問題。本文基于整數(shù)階多智能體系統(tǒng)可控性和分數(shù)階微分的基礎上,研究更貼近自然現(xiàn)象和生活實際的分數(shù)階多智能體系統(tǒng)的可控性。運用現(xiàn)代控制理論、矩陣理論和圖論等基礎知識對一類分數(shù)階多智能體系統(tǒng)的可控性進行分析和研究研究。本文的主要研究內(nèi)容和結論總結如下:1.我們提出了一個新的模型,即分數(shù)階多智能體系統(tǒng),并探究了具有單leader的分數(shù)階多智能體系統(tǒng)在無向圖上的可控性。研究表明具有單leader的分數(shù)階多智能體系統(tǒng)的可控性依賴于leader傳遞給fo llowers的信息,跟fo l lowers的運動軌跡無關,我們得出判斷系統(tǒng)可控的一些充分和必要條件,并給出實例和仿真模擬以驗證理論的正確性。2.分別考慮具有單leader帶時延的時變和時不變的分數(shù)階多智能體系統(tǒng)的可控性問題。在研究的過程中,我們得出了帶時延分數(shù)階系統(tǒng)的可控制僅有l(wèi)eader傳遞給followers的信息決定,并且代數(shù)秩判據(jù)判斷系統(tǒng)的可控時,與階數(shù)α和時延h無關。而且我們通過代數(shù)秩判據(jù)將帶時延的分數(shù)階系統(tǒng)轉化為無時延的分數(shù)階多智能體系統(tǒng)進行進一步研究。得出一些高效的方便計算系統(tǒng)可控性的充分條件。與此同時,我們在文中討論了很多關于特殊拓撲結構之上的分數(shù)階多智能體系統(tǒng)的可控性問題。我們還探究了時變分數(shù)階多智能體系統(tǒng)在切換拓撲下的可控性。而且給出實例和仿真模擬驗證了理論結果。3.探討由一階積分智能體和二階積分智能體構成的異質多智能體系統(tǒng)的可控性問題�？紤]將一階智能體看做leaders,得出此時異質系統(tǒng)在無向圖上可控的充要條件。還考慮了將二階智能體看做leaders,得出此時異質系統(tǒng)在無向圖上可控的充要條件。
[Abstract]:The controllability of fractional multi-agent system has become a hot issue in the research of agent system. This paper based on the controllability and fractional differential of integer order multi-agent system. This paper studies the controllability of fractional multi-agent system, which is closer to natural phenomena and the reality of life, and applies modern control theory. The controllability of a class of fractional multi-agent systems is analyzed and studied based on matrix theory and graph theory. The main contents and conclusions of this paper are summarized as follows: 1. We propose a new model. That is, fractional multi-agent system. The controllability of fractional multi-agent system with single leader on undirected graph is discussed. It is shown that the controllability of fractional multi-agent system with single leader depends on leader transmission. Pass it to fo. Information about llowers. Having nothing to do with the trajectory of Fol lowers, we obtain some necessary and sufficient conditions for judging the controllability of the system. Examples and simulation are given to verify the correctness of the theory. 2. The controllability of fractional multi-agent systems with time-varying and time-invariant time delay with single leader is considered respectively. We obtain that the controllable control of fractional order systems with time delay is determined only by the information transmitted by leader to followers, and the algebraic rank criterion is used to determine the controllable time of the system. It is independent of order 偽 and delay h. Furthermore, we transform fractional order system with delay into fractional multi-agent system without delay by algebraic rank criterion. Some efficient and convenient computing systems can be obtained. Sufficient conditions for controllability. At the same time. In this paper, we discuss the controllability of fractional order multi-agent systems with special topology. We also investigate the controllability of time-varying fractional multi-agent systems under switching topology. An example and simulation results are given to verify the theoretical results. 3. The controllability of heterogeneous multi-agent systems composed of first-order integration agent and second-order integration agent is discussed. The first-order agent is considered as leaders. The necessary and sufficient conditions for the heterogeneity system to be controllable on an undirected graph are obtained, and the necessary and sufficient conditions for the heterogeneity system to be controllable on an undirected graph are obtained by considering the second-order agents as leaders.
【學位授予單位】：北方工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP18

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