基于事件驱动的二次凸优化问题分布式优化算法

Distributed event-triggered algorithm for quadratic convex optimization problem

针对多智能体系统中等式约束下的二次凸优化问题,给出一种事件驱动机制下的分布式优化算法.该算法可以降低每个智能体控制协议的更新频率以及智能体之间的通信负担.基于图论和李雅普诺夫函数方法给出两种不同的事件触发条件,其中第2种事件触发条件不需要拉普拉斯矩阵的最大特征根的信息,可实现算法全分布式实施.两种事件触发条件均可实现算法渐近收敛到优化值,避免智能体控制协议的连续更新以及智能体之间的连续通信,同时保证每个智能体相邻事件触发时刻的时间间隔大于0,避免持续事件触发.将所提出的算法应用于Matlab仿真环境中进行仿真验证,仿真结果验证了所提出算法的有效性.

This paper investigates the quadratic convex optimization problem with equality constraint for multi-agent systems(MASs). In order to reduce the controllers’ update frequency and the communication burden among agents,a distributed event-triggered optimization algorithm is proposed. Based on the graph theorem and Lyapunov function method, two different event-triggered conditions are designed, which guarantee that agents can asymptotically converge to their optimal values. Especially, the second event-triggered condition dose not require the information of the largest eigenvalue of the Laplacian matrix, and thus the algorithm can be implemented in a fully distributed way. The continuous update of controllers and the continuous communication among agents are not required. Meanwhile, the interval of any two contiguous event trigger instants of each agent is more than zero, and continuous event triggering is avoided. Finally,the proposed algorithm is verified in the Matlab simulation environment, and the result of numerical simulation shows the effectiveness of the proposed algorithm.