Average Consensus Tracking of Multi-Agent Systems via Pinning Control

This paper proposes a novel distributed average tracking (DAT) framework for first-order multi-agent systems under directed communication topologies via pinning control strategy. Addressing the challenge of tracking time-varying reference signals with zero steady-state error, we develop an innovative containment feedback control protocol that integrates matrix transformation techniques with adaptive pinning mechanisms. The protocol design incorporates two key components: (i) local interaction terms governed by graph Laplacian matrix, and (ii) adaptive pinning gains for selected agents. Through rigorous Lyapunov stability analysis, we establish sufficient conditions for achieving average consensus tracking, particularly demonstrating that the convergence criterion depends on the spectral properties of the modified Laplacian matrix and pinning gain matrix. A comprehensive simulation study involving three distinct nonlinear dynamics (linear, sinusoidal, and time-varying cosine functions) validates the theoretical findings. Notably, our approach overcomes limitations in existing PI-based methods by guaranteeing asymptotic convergence even for non-constant reference signals. The results reveal that the proposed method maintains consistent convergence speed across different nonlinearities, determined primarily by the network’s adjacency matrix structure.