Leader-following scaled consensus of multi-agent systems based on nonlinear parabolic PDEs via dynamic event-triggered boundary control

Abstract

The aim of this work is to propose a dynamic event-triggered boundary control (DETBC) strategy to investigate the leader-following exponential scaled consensus (SC) problem for multi-agent systems (MASs) under the parabolic partial differential equations (PDEs) framework. Towards this aim, a novel DETBC protocol with Neumann-type boundary conditions is designed, which only needs the information of agents at the boundary $x=l$ rather than the entire spatial domain. Moreover, the adoption of dynamic threshold in the event-triggered mechanism can effectively diminish the frequency of controller updates to bring down the communication loads and economize on control charges. Subsequently, several sufficient conditions to ensure the realization of leader-following SC are acquired in terms of linear matrix inequalities (LMIs) through the Lyapunov method and Wirtinger's inequality. Meanwhile, it is demonstrated that Zeno behavior can be excluded by the devised DETBC strategy. Eventually, some numerical experiments are framed to evaluate the theoretical results.