一类分数阶多智能体系统的可控性研究

发布时间：2018-01-17 22:11

本文关键词：一类分数阶多智能体系统的可控性研究　出处：《北方工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：分数阶多智能体系统的可控性已经成为研究智能体系统的一个热点问题。本文基于整数阶多智能体系统可控性和分数阶微分的基础上,研究更贴近自然现象和生活实际的分数阶多智能体系统的可控性。运用现代控制理论、矩阵理论和图论等基础知识对一类分数阶多智能体系统的可控性进行分析和研究研究。本文的主要研究内容和结论总结如下:1.我们提出了一个新的模型,即分数阶多智能体系统,并探究了具有单leader的分数阶多智能体系统在无向图上的可控性。研究表明具有单leader的分数阶多智能体系统的可控性依赖于leader传递给fo llowers的信息,跟fo l lowers的运动轨迹无关,我们得出判断系统可控的一些充分和必要条件,并给出实例和仿真模拟以验证理论的正确性。2.分别考虑具有单leader带时延的时变和时不变的分数阶多智能体系统的可控性问题。在研究的过程中,我们得出了带时延分数阶系统的可控制仅有leader传递给followers的信息决定,并且代数秩判据判断系统的可控时,与阶数α和时延h无关。而且我们通过代数秩判据将带时延的分数阶系统转化为无时延的分数阶多智能体系统进行进一步研究。得出一些高效的方便计算系统可控性的充分条件。与此同时,我们在文中讨论了很多关于特殊拓扑结构之上的分数阶多智能体系统的可控性问题。我们还探究了时变分数阶多智能体系统在切换拓扑下的可控性。而且给出实例和仿真模拟验证了理论结果。3.探讨由一阶积分智能体和二阶积分智能体构成的异质多智能体系统的可控性问题。考虑将一阶智能体看做leaders,得出此时异质系统在无向图上可控的充要条件。还考虑了将二阶智能体看做leaders,得出此时异质系统在无向图上可控的充要条件。
[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 伪 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.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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