A Novel Edge Laplacian-Based Approach for Adaptive Formation Control of Uncertain Multiagent Systems With Unified Relative Error Performance

Most existing prescribed performance formation control methods impose performance requirements on the consensus error rather than directly on the relative states between agents, which limits the physical interpretability of their solutions. This article proposes a novel adaptive prescribed performance formation control strategy that ensures prescribed performance of relative errors in uncertain high-order multiagent systems under both directed and undirected graphs. Since performance constraints are considered for relative errors, the error dynamics involve a coupled nonlinear interaction term that contains global graphical information among agents, making the design of a fully distributed control strategy more challenging. By proposing a series of nonlinear mappings and utilizing the edge Laplacian along with Lyapunov stability theory, the presented formation control scheme offers several advantages over existing approaches. Different performance requirements can be accommodated in a unified manner by solely tuning the design parameters a priori, eliminating the need for control redesign and stability reanalysis under the proposed fixed control protocol. This enhances user-friendliness and reduces implementation complexity. Furthermore, the verification process for the initial constraint, which is often complex and burdensome in existing prescribed performance control methods, is entirely avoided when the performance requirements are global. Additionally, the proposed approach fully decouples nonlinear interactions and ensures the asymptotic stability of the formation manifold through an adaptive parameter estimation technique. The effectiveness of the theoretical results is demonstrated through simulations.