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.

中文翻译：

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受扰二阶多智能体系统的分布式有限时间优化


在本文中，研究了具有扰动的二阶多智能体系统的分布式有限时间优化问题。为了解决这个问题，建立了前馈-反馈复合控制框架，该框架包含两个主要阶段。第一阶段，针对具有一般强凸成本函数的受扰二阶个体系统，提出了一种基于添加功率积分器和有限时间扰动观测器技术相结合的复合有限时间优化控制方案，并利用成本函数的梯度和 Hessian 矩阵。第二阶段基于第一阶段的结果，针对具有二次局部代价函数的受扰二阶多智能体系统，建立了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的局部成本函数的速度、梯度和 Hessian 矩阵，以及以下形式的一些优化项第一阶段提出的优化控制器基于分布式估计器的估计。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的控制框架的有效性。