Event-triggered practical prescribed-time consensus control for high-order nonlinear multi-agent systems

This work deals with the event-triggered practical prescribed-time consensus tracking for high-order multi-agent systems (MASs) under undirected topologies. Existing prescribed-time control methods for such systems often rely on monotonically increasing functions, which substantially complicates the verification of input-to-state stability within an event-triggered framework. To overcome this limitation, a backstepping-based control strategy is proposed, effectively circumventing the stringent input-to-state stability requirement post-triggering. A first-order filter is also developed to facilitate prescribed-time convergence while substantially reducing computational complexity. Building upon this foundation, the paper provides a rigorous analysis of the coupling between filter frequency and prescribed-time function, deriving stability criteria to guarantee convergence within predefined temporal bounds. Furthermore, a nonlinear-resilient dynamic event-triggered mechanism (NRDETM) is established. Collectively, these techniques guarantee that the consensus tracking errors converge to user-defined bounds within the prescribed time and remain uniformly ultimately bounded thereafter. Finally, the controller's performance under different prescribed times and the efficiency of the proposed event-triggered mechanism (ETM) are demonstrated by numerical examples.