模糊多智能體系統(tǒng)的H_∞一致跟蹤控制

于家鳳 李沁生 邢文 韓春松 馮茂巖

摘要

本文研究非線性多智能體系統(tǒng)在有向拓?fù)湎碌念I(lǐng)導(dǎo)跟隨H∞一致性問題.首先，提出一種新的多項(xiàng)式模糊建模方法來描述由領(lǐng)導(dǎo)者與跟隨者構(gòu)建的偏差動態(tài)系統(tǒng).然后，設(shè)計一致控制協(xié)議使跟隨者漸近跟蹤領(lǐng)導(dǎo)者的軌跡.基于多項(xiàng)式李雅普諾夫函數(shù)技術(shù)，提出松弛的漸近一致的充分條件并確保存在外界干擾時多智能體系統(tǒng)具有H∞抑制性能.將導(dǎo)出的條件轉(zhuǎn)化為平方和形式并能夠進(jìn)行數(shù)值求解.最后，給出一個實(shí)例來驗(yàn)證所提出的一致控制協(xié)議的有效性.關(guān)鍵詞

多智能體系統(tǒng);模糊模型;H∞一致性;有向拓?fù)?/p>

中圖分類號 TP273

文獻(xiàn)標(biāo)志碼 A

0 引言

T-S模糊模型被認(rèn)為是能夠以任意精度逼近光滑非線性系統(tǒng)的一個有效工具[1-2]，得到了廣泛的關(guān)注[3-4].近年來，多項(xiàng)式模糊模型被提出用來建模非線性系統(tǒng)[5]，可看作T-S模糊模型的一種推廣.多項(xiàng)式模糊模型得到了廣泛的關(guān)注，例如，采用平方和方法的多項(xiàng)式模糊控制系統(tǒng)的控制研究[6-7].

另一方面，由于多智能體系統(tǒng)廣泛的應(yīng)用性和顯著的擴(kuò)展性，多智能體系統(tǒng)的一致問題不斷吸引著研究者們的興趣，包括集群控制、群集控制、編隊(duì)控制、復(fù)雜網(wǎng)絡(luò)同步和通信網(wǎng)絡(luò)的擁塞控制[8-9].采用多種控制方法以實(shí)現(xiàn)多智能體的一致，例如自適應(yīng)控制[10-11] 、事件觸發(fā)控制[8，12]、滑?？刂芠13]、H∞控制[7，14].特別地，文獻(xiàn)[14]研究了T-S模糊多智能體系統(tǒng)在無向拓?fù)湎碌念I(lǐng)導(dǎo)跟隨H∞一致控制問題.文獻(xiàn)[7]研究了多項(xiàng)式模糊多智能體系統(tǒng)在無向拓?fù)湎碌念I(lǐng)導(dǎo)跟隨H∞一致控制問題.為了在模糊模型中處理系統(tǒng)狀態(tài)，文獻(xiàn)[7，14]提出了一些嚴(yán)格的假設(shè)條件.

受文獻(xiàn)[7，14]啟發(fā)，本文研究非線性多智能體系統(tǒng)在有向拓?fù)湎碌念I(lǐng)導(dǎo)跟隨H∞一致性問題.首先，建立一個多項(xiàng)式模糊模型來描述領(lǐng)導(dǎo)-跟隨構(gòu)成的非線性多智能體系統(tǒng)，去除了文獻(xiàn)[7，14]的一些假設(shè)條件.進(jìn)一步，設(shè)計了一個新的控制協(xié)議以確保多智能體系統(tǒng)達(dá)到一致.將提出的多項(xiàng)式模糊模型應(yīng)用于非線性多智能體系統(tǒng)的H∞一致控制問題，即在預(yù)設(shè)的一個H∞性能指標(biāo)下，設(shè)計一個H∞控制協(xié)議以實(shí)現(xiàn)跟隨者和領(lǐng)導(dǎo)者一致.基于多項(xiàng)式李雅普諾夫函數(shù)進(jìn)行穩(wěn)定性分析，推導(dǎo)出的多項(xiàng)式矩陣不等式條件轉(zhuǎn)化為平方和（SOS）[15]的條件并進(jìn)行數(shù)值求解.

4 結(jié)論

本文研究了有向拓?fù)湎碌姆蔷€性多智能體系統(tǒng)的H∞一致跟蹤控制問題.首先，提出了一種新的多項(xiàng)式模糊建模方法來描述非線性偏差系統(tǒng)，推導(dǎo)出了基于SOS松弛的H∞一致的充分條件.本文所設(shè)計的狀態(tài)反饋控制協(xié)議能保證多智能體系統(tǒng)實(shí)現(xiàn)漸近一致并滿足設(shè)定的干擾抑制H∞性能指標(biāo).仿真實(shí)例驗(yàn)證了理論結(jié)果的有效性.

參考文獻(xiàn)

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Fuzzy-model-based H∞ consensus tracking

control of multi-agent systems

YU Jiafeng1，2 LI Qinsheng1，3 XING Wen4 HAN Chunsong5 FENG Maoyan1

1 School of Marine & Electrical & Intelligent Engineering，Jiangsu Maritime Institute，Nanjing 211170

2 School of Electrical and Electronic，The University of Adelaide，Adelaide SA 5005，Australia

3 School of Mechatronic Engineering and Automation/Shanghai Key Laboratory of

Power Station Automation Technology，Shanghai University，Shanghai 200072

4 College of Automation，Harbin Engineering University，Harbin 150001

5 School of Mechanical and Electrical Engineering，Qiqihar University，Qiqihar 161002

Abstract This paper is concerned with the H∞ consensus problem for nonlinear leader-follower multi-agent systems （MASs） with a directed communication network.A polynomial fuzzy modeling approach is proposed to describe the error system which is formulated by leader and follower agents.Then，the consensus control protocols are designed for MASs to enforce all the followers to track the trajectory of a leader asymptotically.Based on the polynomial Lyapunov function method，sufficient conditions are presented to ensure the consensus for MASs subject to external disturbances.The obtained conditions are converted into sum of squares and can be numerically solved.Finally，a simulation example is provided to demonstrate the effectiveness of the derived theoretical results.

Key words multi-agent systems;fuzzy modeling;H∞ consensus;directed topology

收稿日期 2020-03-02

資助項(xiàng)目 江蘇省自然科學(xué)基金（BK20191457）;江蘇省現(xiàn)代教育技術(shù)研究課題（61980）重點(diǎn)項(xiàng)目;黑龍江省自然科學(xué)基金（F2017028）;黑龍江省省屬高等學(xué)?；究蒲袠I(yè)務(wù)費(fèi)科研項(xiàng)目（135109242，135409426，135409102）

作者簡介于家鳳，女，博士，研究方向?yàn)槟：刂婆c復(fù)雜動態(tài)網(wǎng)絡(luò)系統(tǒng).yyujie99@163.com