Distributed and adaptive triggering control for networked agents with linear dynamics

This paper proposes distributed event-triggered schemes for achieving state consensus for multi-agent linear systems. For each agent modeled by a linear control system in Rⁿ, a positive signal is embedded in its event function, with the aim of guaranteeing an asymptotic convergence to state consensus for networked linear systems interacted in an undirected and connected graph, and with Zeno triggering excluded for all the agents. The proposed distributed event-based consensus algorithm allows each agent to update its own control at its own triggering times instead of using continuous updates, which thereby avoids complicated computation steps involving data fusion and matrix exponential calculations as used in several event-based control schemes reported in the literature. We further propose a totally distributed and adaptive event-based algorithm, in the sense that each agent utilizes only local measurements with respect to its neighboring agents in its event detection and control update. In this framework, the proposed algorithm is independent of any global network information such as Laplacian matrix eigenvalues associated with the underlying interaction graph. A positive L¹ signal function is included in the adaptive event-based algorithm to guarantee asymptotic consensus convergence and Zeno-free triggering for all the agents. Simulations are provided to validate the performance and superiority of the developed event-based consensus strategies.