一阶多智能体受扰系统的自抗扰分布式优化算法
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陕西师范大学 数学与统计学院,西安 710119

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E-mail: zhiliangzhao@snnu.edu.cn.

中图分类号:

TP273

基金项目:

国家自然科学基金项目(61973202,62003202);流程工业综合自动化国家重点实验室联合项目(2019-KF-23-09).


Active disturbance rejection distributed optimization algorithm for first-order multi-agent disturbance systems
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College of Mathematics and Statistics,Shaanxi Normal University,Xián 710119,China

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    摘要:

    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.

    Abstract:

    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.

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段书晴,陈森,赵志良.一阶多智能体受扰系统的自抗扰分布式优化算法[J].控制与决策,2022,37(6):1559-1566

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  • 在线发布日期: 2022-04-22
  • 出版日期: 2022-06-20