Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach

TLDR

The authors propose an edge‑based fixed‑time consensus protocol for distributed optimization of multi‑agent systems, aiming to minimize the sum of local convex cost functions. The protocol is designed for both time‑invariant and time‑varying cost functions—using Hessian information for the latter—and includes stability conditions that guarantee convergence under fixed and switching communication topologies. They show that the consensus settling time has an upper bound independent of initial states and can be tuned arbitrarily small, enabling applications such as drone rendezvous and battery‑pack power‑output agreement, as demonstrated in case studies.

Abstract

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.