二阶非线性多智能体系统有限时间分布式优化  

Finite-time distributed optimization of second-order nonlinear multi-agent systems

作　　者：娄如思 王璐瑶 马丹[1] LOU Ru-si;WANG Lu-yao;MA Dan(College of Information Science and Engineering,Northeastern University,Shenyang Liaoning 110819,China)

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819

出　　处：《控制理论与应用》2021年第7期1015-1022,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(61973060);辽宁省创新人才支持计划项目(LR2018067)资助。

摘　　要：本文研究一类具有未知常参数的二阶非线性多智能体系统的有限时间自适应分布式优化.首先,通过给定各个智能体的二次目标函数,并结合多智能体系统达到一致性的条件,构造含有惩罚因子的惩罚函数,提出加速智能体状态收敛至目标函数最优解的控制策略.其次,在给定惩罚因子下,基于幂积分方法和有限时间稳定理论,设计有限时间分布式自适应控制协议,使得惩罚函数的梯度在有限时间内收敛到零的邻域内.再次,通过增大惩罚因子,保证多智能体系统的状态最终达到一致,并收敛到总体目标函数的最优解.最后,仿真算例验证了结果的可行性和有效性.This paper investigates the finite-time adaptive distributed optimization for a class of second-order nonlinear multi-agent systems with unknown constant parameters.First of all,a penalty function with a penalty parameter is constructed by providing a quadratic objective function for each agent and integrating consensus conditions of the multi-agent systems.A control strategy,which can accelerate the convergence rate to the optimal solution of the objective function,is also proposed.Secondly,for a given penalty parameter,a finite-time distributed adaptive control protocol is proposed to achieve the bounded consensus of the penalty function’gradient in a finite-time by integrating the power integral method and the finite time stability theory.Thirdly,by increasing the penalty parameter,the state of the multi-agent system can be ensured to achieve consensus asymptotically,which is also the optimal solution of the whole objective function.Finally,simulation results demonstrate the feasibility and effectiveness of the proposed methods.

关 键 词：二阶多智能体系统 未知参数 有限时间 自适应 分布式控制 优化算法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]