基于多智能体系统的分布式凸优化算法研究

In recent years, consensus problems for multi-agent systems have attracted a lot of attention, however, the research of related distributed convex optimization algorithms is still in its primary stage. In this project, distributed convex optimization algorithms with inexact projection, gradient-free information, and quantized information will be considered respectively, under the framework of consensus problems in multi-agent systems; by using convex optimization theory, the convergence properties of the algorithms will be fully analyzed, and the convergence rates of the algorithms will also be characterized. Focusing on the subject of distributed convex optimization algorithms, the aim of this project is to improve some existing theoretical results and investigate some new problems. During the research process, the effects of agents' limited data processing abilities and the network topologies on distributed convex optimization algorithms will be fully considered; special attention will be paid on reducing the requirements of agents' data processing abilities and relaxing the constraint on global information, and investigating the effects of quantized information on the algorithms. Therefore, the proposed algorithms are more suitable to the multi-agent systems than the existing algorithms. The problems investigated in this project are from the literature on consensus problems in multi-agent systems, which is a hot topic in the control community, and therefore, this confirms to the development trend of this subject.

近年来，多智能体系统的一致性问题受到了广泛的关注，但是，与之相关的分布式凸优化算法研究仍处于起步阶段。本项目拟在多智能体系统一致性问题的框架下，分别提出基于不精确投影、免梯度信息和量化信息的分布式凸优化算法；借助凸优化理论，深入研究算法的收敛性质，并刻画算法的收敛速度。本项目的研究目的是，围绕多智能体系统的分布式凸优化算法这一主题，改进或者补充现有相关理论研究结果并探讨新问题。本项目在研究过程中充分考虑智能体有限的数据处理能力和通信网络的拓扑结构对分布式凸优化算法的影响，着重降低算法对智能体自身数据处理能力的要求以及算法对通信网络全局信息的依赖，并探讨信息量化对算法的影响，因而所提出的算法更符合实际多智能体系统的特点。本项目选题紧密围绕多智能体系统一致性问题这一控制科学领域的热点问题，顺应了该学科的发展趋势。

近年来，基于多智能体系统的分布式优化问题因其在诸多实际领域的良好应用前景而受到了广泛的研究关注。本项目在多智能体系统一致性问题的框架下，分别提出基于近似投影、免梯度信息和带不等式约束的多种有效的分布式凸优化算法。借助凸优化理论，深入研究算法的收敛性质，特别地，给出了算法的收敛速度。本项目在研究过程中充分考虑智能体有限的数据处理能力和通信网络的拓扑结构对分布式凸优化算法的影响，着重降低算法对智能体自身数据处理能力的要求以及算法对通信网络全局信息的依赖；与现有算法相比，具有更低的计算复杂度，因而更适于在分布式环境中实现。我们给出了仿真报告结果证明所提出算法的有效性。