Flocking of networked mechanical systems: As new perspective

In this paper, we investigate the flocking problem for multiple uncertain mechanical systems interconnected on digraphs containing a directed spanning tree. To resolve this problem, 1) we propose an integral-sliding based adaptive control to realize flocking, which gives rise to a cascade closed-loop system, and 2) propose a new notion-iBIBO (integral-bounded-input bounded-output) stability to characterize a new input-output property of a special class of dynamical systems, which is then used for the stability analysis of the closed-loop system. With the proposed iBIBO analysis tool and Lyapunov-like approach, we show that the cascade of the flocking subsystem with an external input and the proposed adaptive controller results in stability of the velocities of the whole networked mechanical systems if and only if the damping is greater than certain lower bound for a given stiffness, and that the velocities of the agents converge to the weighted average velocity of the networked mechanical agents and the positions of the agents converge to the initial-condition-dependent ramp trajectory. Simulation results are provided to demonstrate the performance of the proposed adaptive controller.