段书晴(1996-), 女, 硕士生, 从事自抗扰控制及应用的研究, E-mail:
陈森, (1992-), 男, 讲师, 博士, 从事自抗扰控制的研究, E-mail:
赵志良(1979-), 男, 教授, 博士生导师, 从事非线性系统与控制、自抗扰控制等研究, E-mail:
研究一类具有未知外部干扰的一阶多智能体系统的分布式优化问题. 在分布式优化任务中, 每个智能体只被容许利用自己的局部目标函数和邻居的状态信息, 设计一个分布式优化算法, 使全局目标函数取得最小值, 其中全局目标函数是所有局部目标函数之和. 针对该问题, 首先提出由扩张状态观测器和优化算法组成的自抗扰分布式优化算法. 其次, 在Lyapunov稳定性的基础上发展新的方法, 对闭环系统的收敛性和稳定性进行严格的证明; 当外部干扰为常值时, 所设计的优化算法能使所有智能体的状态指数收敛到全局目标函数的最小值; 当外部干扰为有界干扰时, 通过调整扩张状态观测器的增益参数, 所设计的优化算法能使所有智能体的状态收敛到全局目标函数最小值的任意小的邻域内. 最后, 仿真结果表明了该优化算法的有效性.
The paper investigates a distributed optimization algorithm for a class of first-order multi-agent systems with unknown external disturbance. In the distributed optimization task, each agent is only allowed to use its own local cost function and the state information of its neighbors to design a distributed optimization algorithm, so that the global cost function which is the sum of all local cost functions obtains the minimum value. To solve this problem, an active disturbance rejection control distributed optimization algorithm which consists of an extended state observer and an optimization algorithm is proposed. Then, based on the Lyapunov stability, a new method is developed to prove the convergence and stability of the closed-loop system rigidly. When the external disturbance is constant, the designed method can make the states of all agents exponentially converge to the minimum of the global cost function. When the external disturbance is bounded, by adjusting the gain parameter of the extended state observer, the designed method can make the states of all agents converge to an arbitrarily small neighbourhood of the global cost function's minimum value. Finally, the simulation results show the effectiveness of the proposed algorithm.
多智能体系统是由各个智能体根据一定的相互作用共同完成工作任务的系统, 具有自主性、容错性、灵活性、可扩展性和协作能力等特点[
随着网络规模和复杂性的不断加大, 如何针对一般化的复杂系统设计分布式优化策略是一个重要问题. 在这个背景下, 人们提出了许多离散时间分布式优化算法[
关于多智能体系统分布式优化中的干扰抑制问题, 已经有了一些研究成果[
自抗扰控制(active disturbance rejection control, ADRC)是Han[
本文考虑含有未知干扰的连续时间多智能体系统的分布式优化问题. 首先, 设计一类扩张状态观测器(extended state observer, ESO)对干扰进行观测. 其次, 基于ESO的观测, 设计带有干扰补偿和局部梯度下降的分布式优化算法. 最后, 通过对所设计的Lyapunov函数分析得到如下结果: 在外部干扰为常值干扰的情况下, 当
智能体之间的信息分享关系可以通过图的语言进行刻画. 图
由凸分析的定义知, 若存在
\begin{spacing}{1.295}
考虑由
其中:
考虑智能体
本文的优化目标是设计分布式控制
介绍分布式优化算法设计之前, 首先给出以下假设.
本节设计ESO以在线估计系统的“总干扰”, 并提出具有干扰补偿能力和局部梯度下降的分布式优化算法.
ESO的设计如下:
其中:
基于ESO对未知外部干扰的在线估计, 设计如下的优化算法:
其中:
基于2.1节给出的ESO和优化算法, 有下述闭环系统:
对于上述闭环系统, 有如下主要结果.
其中
其中:
推论1说明, 当
本节给出闭环系统(5)的稳定性证明. 首先, 介绍几个重要的引理.
下面证明定理1.
其中
其中
由上述定义, 系统(10)可以写为如下形式:
当外部干扰
其中
考虑系统(12), 若假设1和假设2成立, 则
根据系统(12)中平衡点与最优值
定义如下变量:
通过上述变换, 系统(11)转化为如下所示的误差系统:
为研究系统(14)的稳定性, 令
其中:
定义
根据式(15)的定义可得
对式(16)两边同时求导, 得到
将式(14)代入(17)的第1式, 可得
由式(13)、
进一步, 可得
将式(16)第1式两边同时左乘
由式(18)和矩阵的结合律可得
结合式(16)中第2式和(19)可得
其中
由式(18)中
由上述讨论可知, 系统(14)经过线性变换(15)可以写为如下形式:
由式(13)和(21)可以得到
下面证明系统(22)的稳定性.
考虑如下所示的
其中:
上述
由
由
由Young不等式可得
综合式(23)和(24)、
结合式(8)、(25)和
因此, 对于任意的
因为
其中
下面证明推论1.
因为
其中
由定理1可知, 当
本节考虑一个具有无向连通拓扑结构, 包含5个个体的多智能体系统, 每个智能体的动态可用系统(1)描述, 其中
智能体的网络拓扑图
取
智能体
由
基于ESO和IM的分布式优化算法下各智能体的状态曲线
本文提出了一种新的抗扰方法来解决具有未知干扰的一阶多智能体系统的分布式优化问题. 针对该问题, 设计了由ESO和优化算法组成的自抗扰分布式优化算法. 在该算法下, 当
责任编委:张国山.
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