基于分段幂律设计的分布式固定时间优化
Distributed Fixed-Time Optimization Based on Piecewise Power-Law Design
摘要: 本文基于幂律算法研究了多智能体系统的固定时间和指定时间优化问题。在成本函数强凸的条件下，提出一种分段幂律算法，保证了智能体先达到固定时间一致再实现固定时间优化。此外，通过设计分段控制协议研究了指定时间优化问题，其中优化完成时间可以根据实际需求任意指定。最后，通过两个数值实例验证了所提算法的有效性。
Abstract: The problem of fixed-time and specified-time optimization of multi-agent systems is investigated in this paper based on power-law algorithms. Under the condition that the cost function is strongly convex, a piecewise power-law algorithm is proposed, which can ensure that the agents reach consensus in a fixed time and then achieve fixed-time optimization. Correspondingly, the problem of specified-time optimization is also studied by designing a piecewise control protocol, in which the optimization time can be arbitrarily specified according to actual requirement. Finally, through two numerical examples, the effectiveness of the proposed algorithms is verified.
文章引用：马兰兰. 基于分段幂律设计的分布式固定时间优化[J]. 理论数学, 2022, 12(4): 549-560. https://doi.org/10.12677/PM.2022.124061

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