Containment Control of Multi-Agent Systems with Prescribed Performance by Using Constraint Allocation and Residual Compensation

This paper investigates prescribed-performance containment control of nonlinear multi-agent systems with multiple leaders under a fixed directed graph. To reconcile follower-specific physical containment envelopes, multi-leader targets determined by the communication graph, and the virtual errors available for distributed feedback, the inverse-Laplacian transfer principle is used to construct sufficient virtual-error bounds. Nonlinear evaluation and convex averaging also generate a possibly nonvanishing nonlinear averaging residual at the containment target. The controller therefore couples the allocated barrier feedback with a directional robust term that dominates this residual in the Lyapunov estimate. For every maximal Filippov solution, a barrier Lyapunov analysis based on an improper integral establishes forward completeness, invariance of the allocated virtual and prescribed physical envelopes, and asymptotic physical containment. Finally, simulation studies across multiple configurations and two direct comparisons with existing methods verify the theoretical results.