Adaptive dynamic event-triggered control for multi-agent systems with matched uncertainties under directed topologies

This paper deals with the consensus problem of linear multi-agent systems (MASs) with matched uncertainties on directed topologies via a dynamic event-triggered control. To reduce the redundant communication, a distributed dynamic event-triggered (DET) protocol with a dynamic threshold is proposed, which makes the average time interval of controller update have a positive lower bound. The Zeno behavior can also be excluded. Furthermore, to avoid the assuming availability of full state information, an observer-based adaptive dynamic event-triggered (ADET) protocol is introduced. The proposed adaptive σ-modification technique for the time-varying coupling gain can render smaller control gain and achieve better regulatory effects. Compared with the existing DET scheme, the dynamic threshold with a positive lower bound can reach consensus with larger inter-execution times and less communication energy among agents. By using the Riccati equation and inequality techniques, some simple and convenient sufficient conditions are derived to guarantee the stability of the closed-loop system. Finally, two numerical examples are given to verify the effectiveness of the obtained theoretical results.