基于多智能体网络的分布式优化研究

发布时间：2024-04-14 07:59

　　分布式优化在无线传感器网络、交通系统、多机器人系统、社交网络及分布式电网等诸多领域有着广泛的应用,因此,近年来分布式优化受到众多学者的关注和青睐。本文综合利用凸分析理论、优化理论、博弈理论、图理论和Lyapunov稳定性理论等工具,研究了基于多智能体网络的分布式优化问题。首先,利用智能体的合作行为研究了局部目标函数和的最优化问题;其次,考虑个体间存在竞争行为的情况,结合非合作博弈理论,研究了一类广义纳什均衡点的分布式求解问题;最后,研究了一类混合均衡问题的分布式求解,为最优化问题和纳什均衡点问题建立了统一的求解框架。本文主要贡献包括以下几个方面:1.研究了具有凸不等式组约束的分布式优化问题。首先,针对凸不等式组的分布式求解问题,基于一致性算法和次梯度算法,提出了一类连续时间的分布式次梯度算法来得到其可行解。研究结果表明:当有向图满足强连通条件时,所有智能体的状态收敛到不等式组的一个可行解。进一步,针对一类具有凸不等式组约束的分布式优化问题,利用鞍点策略和一致性算法,提出了一类连续时间的分布式算法。当时变有向图满足δ-强连通条件时,多智能体系统达到一致,且一致性状态为该约束优化问题的最优...

【文章页数】：113 页

【学位级别】：博士

【文章目录】：
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



本文编号：3954364