Distributed Optimization of Multiagent Systems Against Unmatched Disturbances: A Hierarchical Integral Control Framework
针对双积分器多智能体系统在恒定非匹配扰动下的分布式优化问题，提出一种基于状态积分反馈和自适应控制的两层框架，上层生成全局最优轨迹，下层实现渐近跟踪，并给出控制参数与通信间隔的协同设计方法。
This article investigates a distributed optimization problem of double-integrator multiagent systems with unmatched constant disturbances. Instead of involving an internal model or a disturbance observer to deal with the disturbances as in existing works, a two-layer control framework is presented based on state-integral feedback control (SIFC) and adaptive control techniques. The upper layer uses a virtual system to generate a global optimal consensus trajectory which is shared by the agents via a communication network. The lower layer includes an SIFC controller to guarantee asymptotic tracking of the given trajectory. Also in this layer, a model reference adaptive controller is introduced to enhance the dynamic tracking performance of the SIFC controller. This framework enables distributed optimization with time-triggered communication and mild requirements on the team objective. The method yields an interesting co-design algorithm of the control parameters and the communication intervals, which is proved to be convergent using Lyapunov stability theory. The effectiveness and advantages of the method are illustrated by numerical simulations.