A Novel Edge Laplacian-based Approach for Adaptive Formation Control of Uncertain Multi-agent Systems with Unified Relative Error Performance

TL;DR

This paper introduces an adaptive formation control method for uncertain multi-agent systems that guarantees prescribed relative error performance using edge Laplacian, simplifying design and ensuring stability.

Contribution

It proposes a novel adaptive control strategy that guarantees prescribed relative error performance with a unified approach, avoiding control redesign and complex initial constraint verification.

Findings

Guarantees prescribed relative error performance via a unified parameter tuning.

Eliminates the need for control redesign under fixed protocols.

Ensures asymptotic stability of the formation manifold.

Abstract

For most existing prescribed performance formation control methods, performance requirements are not directly imposed on the relative states between agents but on the consensus error, which lacks a clear physical interpretation of their solution. In this paper, we propose a novel adaptive prescribed performance formation control strategy, capable of guaranteeing prescribed performance on the relative errors, for uncertain high-order multi-agent systems under a class of directed graphs. Due to the consideration of performance constraints for relative errors, a coupled nonlinear interaction term that contains global graphic information among agents is involved in the error dynamics, leading to a fully distributed control design more difficult and challenging. Here by proposing a series of nonlinear mappings and utilizing the edge Laplacian along with Lyapunov stability theory, the presented formation control scheme exhibits the following appealing features when compared to existing results: 1) different performance requirements can be guaranteed in a unified way by solely tuning the design parameters a priori, without the need for control redesign and stability reanalysis under the proposed fixed control protocol, making the design more user-friendly and the implementation less demanding; 2) the complex and burdensome verification process for the initial constraint, often encountered in existing prescribed performance controls, is completely obviated if the performance requirements are global; and 3) nonlinear interaction is completely decoupled and the asymptotic stability of the formation manifold is ensured via using the adaptive parameter estimate technique. Finally, simulations of various performance behaviors are performed to show the efficiency of the theoretical results.