Event-Triggered Adaptive Consensus Tracking Control of Uncertain Nonlinear Multi-agent Systems with Uniformly Positive Inter-Event Times

In this paper, asymptotical consensus tracking control problem is considered for a class of uncertain nonlinear multi-agent systems under directed graph with event-triggered communication. In this work, the main challenge is to handle cross-coupling term associated with unknown parameters of all agents and asymmetric Laplacian matrix when the Lyapunov function candidate is selected in terms of local consensus errors. This leads to the difficulty in designing distributed asymptotical control laws which can guarantee a positive minimum inter-event time for each agent with event-triggered communication. To handle this issue, an event-triggered based control scheme is proposed by applying adaptive immersion & invariance control and concurrent learning adaptive control. We prove that all closed-loop signals are uniformly bounded, and all agents’ states can exponentially track the desired trajectory. Moreover, the inter-event times of all agents are uniformly lower bounded by a positive constant. Finally, an illustrative example is given to validate the effectiveness of the proposed control scheme.