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

中文关键词  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

英文关键词  second-order multi-agent systems  unknown parameters  finite-time  adaptive control  distributed control  optimization algorithm

中文摘要

      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.

英文摘要

      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.