Fixed-Time Periodic Dynamic Event-Based Fuzzy Control for Multi-Target Encircling of Underactuated Surface Vehicles

This paper investigates the multi-target encircling event-based fuzzy control of uncertain underactuated surface vehicles (USVs) subject to input delay, where the delay is characterized through Pade approximation. The distributed fixed-time estimators are designed to obtain the positions and velocities of the targets. Using the estimated information, encircling velocities are generated for each USV with the multi-target center serving as the reference point. To address system uncertainties, fuzzy logic systems are employed to approximate unknown nonlinear dynamics, while a fixed-time fuzzy control scheme incorporating a periodic dynamic event-triggered mechanism is introduced to accomplish the multi-target encircling task. The theoretical validity of the proposed methodology is rigorously established through Lyapunov function analysis. Numerical simulations further validate both the efficacy and advantages of the developed control strategy.