Adaptive Asymptotic Synchronization With Unified Performance for Uncertain Multi-Agent Systems Using a Fixed Control Structure

Achieving leaderless asymptotic synchronization for uncertain multi-agent systems while guaranteeing prescribed transient performance remains a significant challenge for traditional methods. This difficulty arises from the redundancy between relative errors and performance functions in nonlinear dynamics, which obscures the explicit expression of local topological information in terms of the Laplacian matrix. In this work, we propose an adaptive asymptotic consensus control with unified prescribed performance for multi-agent systems, which exhibits several notable features. Firstly, we construct a homeomorphic function transformation for the relative error, enabling multiple prescribed performance behaviors to be maintained under a fixed control structure. Secondly, we establish a quantitative relationship between the transformed error and the relative error, revealing the lower bound of the transformed error-based normalized Jacobian, which is crucial for asymptotic control design. Thirdly, we introduce a robust decomposition technique in the developed lemma, allowing the redundancy to be split into two independent components. By incorporating a negative feedback element into the proposed controller and utilizing a parameter estimation technique, we further compensate the redundancies and guarantee the asymptotic stability of the closed-loop system. Simulation results illustrate the effectiveness of the proposed control scheme.