分布式有限时间最优化问题

With the rapid development of computer science and communication technology, there appear more and more new networked systems in the distributed context. Due to its centralized fasion, traditional optimization theory is difficult to apply to these networked systems, especially for some systems that are concerned about the optimal convergence rate.. The objective of our proposal is to study the distributed finite-time optimization problems under various constraints. Detailed contents are as follows: . For multi-agent systems without state constraints, a distributed algorithm will be introduced, and the coupling relationship between the optimal convergence and the consensus convergence of the system will be investigated. Then, conditions will be given to ensure the finite-time optimal convergence of the global objective function and the effects of the parameters of the algorithm will be analyzed on the optimal convergence and the system stability.. For multi-agent systems without state convex-set constraints, a distributed algorithm will be designed, and the effects of the nonlinearity of the convex-set constraints will be studied on the optimal convergence of the system. Then, conditions will be given to ensure the finite-time optimal convergence of the global objective function and the effects of the parameters of the algorithm will be analyzed on the optimal convergence and the system stability.. For multi-agent systems with asynchronous stepsizes, a distributed algorithm will be designed, and the effects of asynchronous stepsizes will be studied on the optimal convergence of the system. Then, conditions will be given to ensure the finite-time optimal convergence of the global objective function and the effects of the parameters of the algorithm will be analyzed on the optimal convergence and the system stability.

随着计算机和通信技术的快速发展，新型分布式网络化系统不断涌现，传统的最优化理论由于其集中式的特点，已难以适用于这些系统，特别是在一些更注重最优收敛快速性的系统中。本项目旨在研究不同约束条件下的分布式有限时间最优化问题，具体内容包括：针对状态无约束多智能体系统，设计分布式算法，研究系统最优收敛性和状态一致收敛性之间的耦合关系，给出系统有限时间最优收敛的条件，并分析算法中各参数对系统最优收敛性和稳定性的影响；针对状态具有凸集约束的多智能体系统，设计分布式算法，重点研究凸集约束特别是非一致凸集约束所引发的非线性对系统最优收敛性的影响，给出系统有限时间最优收敛的条件，并分析算法中各参数对系统最优收敛性和稳定性的影响；针对最优收敛步长异步的多智能体系统，设计分布式算法，重点研究最优收敛步长的异步性对系统最优收敛的影响，给出系统有限时间最优收敛的条件，并分析算法中各参数对系统最优收敛性和稳定性的影响。

随着计算机和通信技术的快速发展，新型分布式网络化系统不断涌现，传统的最优化理论由于其集中式的特点，已难以适用于这些系统，特别是在一些更注重最优收敛快速性的系统中。针对分布式有限时间最优化问题，先后研究了具有非一致状态凸集约束分布式最优化问题和异步完全分布式最优化问题。并在此基础上，拓展研究了非凸受限分布式一致性问题和拓扑结构切换具有时滞的分布式包含控制问题。在算法设计和系统稳定性分析方面，开展了深入研究，取得了一批成果。所得相关结果17篇论文发表在国际权威期刊上，包括IEEE Transactions 9篇(TAC 6篇，TIE 1篇，TC 2篇)，Automatica 1篇。4篇论文入选ESI高被引论文。相关成果受到了10位院士和31位IEEE Fellow/IFAC Fellow的正面引用，4篇论文先后入选ESI高被引论文。在此项目基础上，项目负责人获2017年度教育部自然科学奖一等奖（排名第2），2017年获批国家自然科学基金重大项目1项(课题负责人)。