Performance Guaranteed Consensus Tracking for Double-Integrator Multiagent Systems via High-Dimensional Error Norm Specification

This article addresses the performance guaranteed consensus tracking problem for high-dimensional double-integrator multiagent systems. By integrating a dynamic surface-based back-stepping method, we propose an edge-based prescribed performance control (PPC) scheme, independent of any topology-related information. Unlike most existing works on the 1-D error constraint, the transient tracking performance in our work is ensured by imposing a constraint on the high-dimensional error norm, thereby avoiding the decoupling of the states. Moreover, a composite predefined time-based performance function is developed to ensure the user-defined settling time and steady-state error accuracy, while relaxing the dependence on initial states. We further establish a unified error transformation framework for the norm-based PPC approach. Lastly, a numerical simulation and a formation application example verify the effectiveness of the proposed control scheme.