Wang Xiangyu, Wang Guodong, Li Shihua
IEEE Trans Cybern. 2021 Sep;51(9):4634-4647. doi: 10.1109/TCYB.2020.2988490. Epub 2021 Sep 15.
In this article, the distributed finite-time optimization problem is investigated for second-order multiagent systems with disturbances. To solve this problem, a feedforward-feedback composite control framework is established, which contains two main stages. In the first stage, for disturbed second-order individual systems with generally strongly convex cost functions, a composite finite-time optimization control scheme is proposed based on the combination of adding a power integrator and the finite-time disturbance observer techniques and the use of the cost functions' gradients and Hessian matrices. In the second stage, based on the result of the first stage, a distributed composite finite-time optimization control framework is built for disturbed second-order multiagent systems with quadratic-like local cost functions. This framework involves a kind of finite-time consensus algorithm, some novel distributed finite-time estimators designed for each agent to estimate the velocity, the gradient and Hessian matrix for the local cost function of any other agent, and some optimization terms in the form of the optimization controllers proposed in the first stage and based on the estimates from the distributed estimators. The finite-time convergence of the closed-loop systems is rigorously proved. The simulation results illustrate the effectiveness of the proposed control framework.
本文研究了具有干扰的二阶多智能体系统的分布式有限时间优化问题。为解决该问题，建立了一种前馈-反馈复合控制框架，该框架包含两个主要阶段。在第一阶段，针对具有一般强凸代价函数的受干扰二阶个体系统，基于添加幂积分器和有限时间干扰观测器技术的结合以及代价函数梯度和海森矩阵的使用，提出了一种复合有限时间优化控制方案。在第二阶段，基于第一阶段的结果，为具有类二次局部代价函数的受干扰二阶多智能体系统构建了一个分布式复合有限时间优化控制框架。该框架涉及一种有限时间一致性算法、为每个智能体设计的一些新颖的分布式有限时间估计器，用于估计任何其他智能体局部代价函数的速度、梯度和海森矩阵，以及基于分布式估计器的估计并采用第一阶段提出的优化控制器形式的一些优化项。严格证明了闭环系统的有限时间收敛性。仿真结果说明了所提出控制框架的有效性。
