Flocking of networked mechanical systems on directed topologies: a new perspective

Abstract

In this paper, we investigate the flocking problem for multiple uncertain mechanical systems interacting on directed topologies. We propose an integral-sliding adaptive control to realise the objective of flocking, which gives rise to a cascade closed-loop system, and also propose a new notion – iBIBO (integral-bounded-input bounded-output) stability to characterise 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 proposed adaptive controller ensures the position and velocity consensus of the mechanical systems if and only if the damping is greater than certain lower bound for a given stiffness, and that the velocities of the mechanical systems converge to the weighted average of their initial values and the positions of the mechanical systems converge to the initial-states-dependent ramp trajectory. The performance of the proposed adaptive control scheme is shown by numerical simulation results.