Adaptive containment control of second-order multi-agent systems with nonlinear dynamics and multiple input-bounded leaders

This paper considers the adaptive containment control problem of second-order multi-agent systems with inherent nonlinear dynamics. In particular, the leaders' control inputs are nonzero, bounded, and not available to any follower. Based on the relative states among neighbouring agents, a discontinuous adaptive protocol is first proposed to ensure that the containment errors of each follower converge to zero asymptotically, i.e. the states of the followers asymptotically converge to the convex hull spanned by those of the leaders. To eliminate the chattering effect caused by the discontinuous protocol, a continuous adaptive protocol is further designed based on the boundary layer technique and the σ-modification technique. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.