Distributed containment control for active leaders with time-varying inputs: PI-based and reset-based approaches

This paper investigates the containment control of double-integrator multi-agent systems with active leaders subject to time-varying inputs. A proportional–integral (PI) containment controller is developed to ensure asymptotic convergence under the disturbances, and a reset-based mechanism is incorporated into the integral term to enhance transient performance without the disturbances. Rigorous stability analyses are provided for both two controllers. It is further proved that the reset-based controller achieves faster convergence than the case without integral term, while each follower possesses regularity in every dimension. Finally, numerical simulations demonstrate the effectiveness and performance advantages of the proposed approaches.