本文關鍵詞： 代數(shù)圖論 時變時滯 多智能體系統(tǒng) 加權(quán)平均一致性 線性矩陣不等式 最優(yōu)控制　出處：《西南交通大學》2017年碩士論文　論文類型：學位論文

【摘要】：在工業(yè)生產(chǎn)中,設備的運行無法達到理想狀態(tài),時滯現(xiàn)象是控制過程中無法避免的問題之一。時滯系統(tǒng)的最優(yōu)控制問題具有很高的研究價值和現(xiàn)實意義,也是近年來控制領域研究的熱點和難點課題之一。一致性問題作為智能體之間協(xié)調(diào)合作的基礎,受到越來越多研究者的關注。所謂"一致性"是指:智能體的某些狀態(tài)變量從一組給定值經(jīng)過一定的時間之后趨于同一值,稱為系統(tǒng)的決策值。而一致性算法就是使得系統(tǒng)中每個智能體的狀態(tài)趨于一致的協(xié)議。本文主要討論了帶有時滯的線性多智能體系統(tǒng)一致性和最優(yōu)控制問題。本論文的主要內(nèi)容和研究成果總結(jié)如下:1.主要對線性時變時滯多智能體網(wǎng)絡的加權(quán)平均一致性問題進行了研究,通過將加權(quán)平均系數(shù)融合進控制器參數(shù)設計,大大方便了多智能體系統(tǒng)的綜合�；诖鷶�(shù)圖論和矩陣分析工具,分別研究了時變時滯多智能體系統(tǒng)在固定和切換網(wǎng)絡拓撲下的加權(quán)平均一致性,利用Lyapunov-Krasovskii理論,以LMI的形式給出了線性控制協(xié)議在網(wǎng)絡拓撲是固定和切換兩種情況下取得加權(quán)平均一致性的充分條件,結(jié)論證明所有的節(jié)點在實現(xiàn)穩(wěn)定時均達到了智能體初態(tài)的加權(quán)平均值。2.研究了具有時滯的一般離散時間多智能體系統(tǒng)的一致性問題,基于李雅普諾夫穩(wěn)定性定理,通過構(gòu)造李雅普諾夫泛函并保留了李雅普諾夫泛函差分中的有用信息,利用線性矩陣不等式方法,給出了系統(tǒng)穩(wěn)定的充分條件,并通過實例計算求出了系統(tǒng)能夠容忍的時滯范圍和滿足系統(tǒng)穩(wěn)定性條件的一組矩陣解,從而驗證了本文所得到的結(jié)論的有效性和可行性。3.研究了線性時滯多智能體系統(tǒng)的最優(yōu)控制問題。首先,針對時滯系統(tǒng)的最優(yōu)狀態(tài)調(diào)節(jié)問題,對于帶時滯的狀態(tài)方程,根據(jù)柯西公式的特性,求出了一個特解,給出了閉環(huán)系統(tǒng)的狀態(tài)線性反饋控制律,并最終得到了最優(yōu)控制器的解的形式。其次,針對時滯多智能體系統(tǒng)在有限時域下的最優(yōu)跟蹤問題,本文將含有輸入時滯的線性系統(tǒng)變換成形式上無時滯的線性系統(tǒng),根據(jù)最優(yōu)控制理論構(gòu)造了 Riccati矩陣方程組,并提出了動態(tài)輸出反饋最優(yōu)跟蹤控制算法。最后,通過計算機仿真實例驗證了本文結(jié)論的正確性和有效性。
[Abstract]:In the industrial production, the operation of the equipment can not reach the ideal state, and the delay phenomenon is one of the unavoidable problems in the control process. The optimal control problem of the time-delay system has high research value and practical significance. It is also one of the hot and difficult topics in the field of control in recent years. Consistency is the basis of coordination and cooperation among agents. More and more researchers pay attention to it. The so-called "consistency" means that some state variables of an agent tend to the same value after a certain time from a given set of values. This paper mainly discusses the consistency and optimal control of linear multi-agent systems with time delay. The main contents and research results are summarized as follows:. 1. The weighted average consistency problem of linear time-varying time-delay multi-agent networks is studied. By integrating the weighted average coefficient into the controller parameter design, the synthesis of multi-agent system is greatly facilitated, based on algebraic graph theory and matrix analysis tool. The weighted average consistency of time-varying time-delay multi-agent systems under fixed and switched network topology is studied, and the Lyapunov-Krasovskii theory is used. In the form of LMI, a sufficient condition is given for the linear control protocol to obtain weighted average consistency when the network topology is fixed and handoff. It is proved that all nodes reach the weighted average of the initial state of the agent. 2. The consistency problem of the general discrete-time multi-agent system with time delay is studied. Based on Lyapunov stability theorem, by constructing Lyapunov Functionals and preserving useful information in Lyapunov functional difference, a sufficient condition for the stability of the system is given by using the method of linear matrix inequality (LMI). A set of matrix solutions which can tolerate the delay range and satisfy the stability condition of the system are obtained by the example calculation. Therefore, the validity and feasibility of the conclusions obtained in this paper are verified. 3. The optimal control problem for linear time-delay multi-agent systems is studied. Firstly, the optimal state adjustment problem for time-delay systems is studied. For the state equation with time delay, according to the characteristic of Cauchy formula, a special solution is obtained, and the state linear feedback control law of the closed-loop system is given, and the form of the optimal controller solution is obtained. To solve the problem of optimal tracking for multi-agent systems with time-delay in finite time domain, a linear system with input time delay is transformed into a linear system with no time delay. According to the optimal control theory, the Riccati matrix equations are constructed, and the dynamic output feedback optimal tracking control algorithm is proposed. The correctness and validity of the conclusion are verified by computer simulation.
【學位授予單位】：西南交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP18;O232

【參考文獻】

相關期刊論文 前4條

1 馬婧瑛;鄭元世;王龍;;多智能體系統(tǒng)的性能優(yōu)化[J];系統(tǒng)科學與數(shù)學;2015年03期

2 張慶杰;沈林成;朱華勇;;具有多個通信時延的一類二階多智能體系統(tǒng)平均一致性[J];控制與決策;2011年10期

3 程代展,陳翰馥;從群集到社會行為控制[J];科技導報;2004年08期

4 胡蓬，，石純一，王克宏;開放的分布式人工智能[J];軟件學報;1995年10期

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