Adaptive containment control algorithm design of second-order multi-agent systems under disturbances

This study addresses the robustness challenges in hierarchical coordination of second-order networked multi-agent systems operating under exogenous perturbations. A decentralized adaptive control framework is developed to dynamically regulate follower agents toward a time-varying convex domain spanned by leaders, with explicit compensation mechanisms for bounded yet unstructured disturbances. Unlike conventional containment strategies relying on fixed-gain feedback, the proposed algorithm integrates a nonlinear sigmoidal adaptation law (Equation 6) that autonomously scales control efforts based on real-time error metrics, ensuring asymptotic convergence without prior knowledge of disturbance bounds. Global stability of the closed-loop system is rigorously proven via a composite Lyapunov function that jointly accounts for state errors and adaptive gain dynamics. Parametric studies further reveal a tunable trade-off between convergence speed and control energy consumption. Experimental validations under heterogeneous disturbance profiles—including non-smooth square waves and stochastic noise—demonstrate superior containment accuracy and rapid settling time.