分布式優(yōu)化在無(wú)線傳感器網(wǎng)絡(luò)、交通系統(tǒng)、多機(jī)器人系統(tǒng)、社交網(wǎng)絡(luò)及分布式電網(wǎng)等諸多領(lǐng)域有著廣泛的應(yīng)用,因此,近年來(lái)分布式優(yōu)化受到眾多學(xué)者的關(guān)注和青睞。本文綜合利用凸分析理論、優(yōu)化理論、博弈理論、圖理論和Lyapunov穩(wěn)定性理論等工具,研究了基于多智能體網(wǎng)絡(luò)的分布式優(yōu)化問(wèn)題。首先,利用智能體的合作行為研究了局部目標(biāo)函數(shù)和的最優(yōu)化問(wèn)題;其次,考慮個(gè)體間存在競(jìng)爭(zhēng)行為的情況,結(jié)合非合作博弈理論,研究了一類廣義納什均衡點(diǎn)的分布式求解問(wèn)題;最后,研究了一類混合均衡問(wèn)題的分布式求解,為最優(yōu)化問(wèn)題和納什均衡點(diǎn)問(wèn)題建立了統(tǒng)一的求解框架。本文主要貢獻(xiàn)包括以下幾個(gè)方面:1.研究了具有凸不等式組約束的分布式優(yōu)化問(wèn)題。首先,針對(duì)凸不等式組的分布式求解問(wèn)題,基于一致性算法和次梯度算法,提出了一類連續(xù)時(shí)間的分布式次梯度算法來(lái)得到其可行解。研究結(jié)果表明:當(dāng)有向圖滿足強(qiáng)連通條件時(shí),所有智能體的狀態(tài)收斂到不等式組的一個(gè)可行解。進(jìn)一步,針對(duì)一類具有凸不等式組約束的分布式優(yōu)化問(wèn)題,利用鞍點(diǎn)策略和一致性算法,提出了一類連續(xù)時(shí)間的分布式算法。當(dāng)時(shí)變有向圖滿足δ-強(qiáng)連通條件時(shí),多智能體系統(tǒng)達(dá)到一致,且一致性狀態(tài)為該約束優(yōu)化問(wèn)題的最優(yōu)...

【文章頁(yè)數(shù)】：113 頁(yè)

【學(xué)位級(jí)別】：博士

【文章目錄】：
ABSTRACT
摘要
List of Symbols
List of Abbreviations
Chapter 1 Introduction
    1.1 Background of Multi-agent Systems
    1.2 Distributed Optimization
        1.2.1 Motivation
        1.2.2 Literature Review
    1.3 Thesis Organization
Chapter 2 Preliminaries
    2.1 Convex Analysis
        2.1.1 Convex Sets
        2.1.2 Convex Functions
    2.2 Optimization Theory
    2.3 Graph Theory
    2.4 Consensus Results
        2.4.1 Continuous-time Case
        2.4.2 Discrete-time Case
Chapter 3 Distributed Optimization with Convex Inequality Constraints
    3.1 A Distributed Algorithm for Solving Convex Inequalities
        3.1.1 Problem Formulation
        3.1.2 The Design of the Distributed Algorithm
        3.1.3 Convergence Analysis
        3.1.4 A Simulation Example
    3.2 Distributed Optimization with Convex Inequality Constraints
        3.2.1 Problem Formulation
        3.2.2 The Design of the Distributed Algorithm
        3.2.3 Convergence Analysis
        3.2.4 A Simulation Example
    3.3 Summary
Chapter 4 Online Distributed Optimization with Pseudoconvex-sum Cost Functions
    4.1 Problem Formulation
        4.1.1 Online Distributed Optimization
        4.1.2 Basic Assumptions
    4.2 The Design of Online Distributed Algorithm
    4.3 Main Results
    4.4 A Simulation Example
    4.5 Summary
Chapter 5 Distributed Algorithms for Seeking Generalized Nash Equilibrium
    5.1 Problem Formulation
        5.1.1 Non-cooperative Games
        5.1.2 Basic Assumptions
    5.2 The Design of the Distributed Algorithm
    5.3 Main Results
    5.4 A Simulation Example
    5.5 Summary
Chapter 6 A Distributed Algorithm for Solving Mixed Equilibrium Problems
    6.1 Introduction
    6.2 Problem Formulation
    6.3 The Design of the Distributed Algorithm
    6.4 Main Result
    6.5 Some Discussions on the Balance Condition
    6.6 A Simulation Example
    6.7 Summary
Chapter 7 Conclusions and Future Research
    7.1 Contributions
    7.2 Future Work
Reference
Acknowledgement
Biography



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