Momentum-Based Distributed Disturbance Feedback Optimization of Heterogeneous Multiagent Systems: A Timescale Separation Approach

In this article, the distributed disturbance feedback optimization problem of the heterogeneous linear multiagent systems is studied. In order to achieve the objective of driving all agents with disturbance to the optimal solution of the global nonconvex objective function, momentum-based distributed feedback optimization coordinators are designed, where the nonconvex objective function and the general dynamics of an agent, and the external disturbance are considered simultaneously. Compared to existing results, which require the form of the gradient function to be known, the proposed distributed feedback optimization coordinators considered only need partial information related to the actual input–output of the local objective functions. This partial information is used to estimate the gradient values at each moment. The overall closed-loop system is an interconnected system involving the module of optimal coordinators and the heterogeneous linear multiagent systems with different timescales and thus is studied by using singular perturbation theory. Finally, the effectiveness and superiority of the proposed method are illustrated by a numerical example and a firefighting robot simulation.