Dynamic event-triggered prescribed-time performance control for stochastic nonlinear multi-agent systems with arbitrary bounded initial errors

This paper investigates the prescribed-time performance control (PTPC) problem for a class of stochastic nonlinear multi-agent systems (MASs) under a dynamic event-triggered mechanism. First, a nonlinear mapping function is introduced and a smooth, continuously differentiable prescribed-time auxiliary function is constructed, such that the tracking error can enter the prescribed performance bounds from any initial error condition. Unlike existing static and dynamic event-triggered schemes, a novel dynamic event-triggered mechanism is developed by combining an auxiliary internal dynamic variable with a bounded time-varying threshold-shaping factor, thereby reducing control-signal transmissions. Furthermore, the designed prescribed-time performance controller can dynamically reset the performance bounds when disturbances violate the prescribed performance constraints, while guaranteeing that all signals in the MASs remain bounded in probability. Finally, two simulation examples verify the effectiveness of the proposed approach.