Adaptive coordination of second-order multi-agent systems with instinct nonlinear dynamics under a directed graph

In this paper, we study the distributed coordination for second-order multi-agent systems with intrinsic nonlinear dynamics and heterogeneous control gains under a general directed graph. Unlike the existing consensus algorithm for second-order multi-agent systems under a directed graph where all agents share common control gains, here we allow the control gains are heterogeneous for each agent. We propose fully distributed consensus algorithms for both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader. Novel integral-type Lyapunov functions are proposed to study the consensus and tracking convergence. The control gains are varying and updated by distributed adaptive laws. As a result, the proposed algorithms require no global information and thus can be implemented in a fully distributed manner.