Tracking Control of Wave-Adaptive Modular Unmanned Surface Vehicle Using Time-Delay Zeroing Neural Network

The advancement of artificial intelligence has significantly enhanced the role of unmanned surface vehicles (USVs) in various ocean engineering applications. Designing a controller for USV systems that ensures stability, high precision, and rapid convergence remains a complex challenge in intelligent control. In this paper, we begin by developing two high-order backward finite difference formulas (BFDFs) with a second-order truncation error. These formulas are used to approximate the second and third derivatives of smooth functions. Building on these innovative BFDFs, we introduce a second-order tracking controller utilizing a multiple zeroing neural network (ZNN) model with time delay to address the tracking control of the wave-adaptive modular vessel’s vertical motion dynamics (WAMV-VMD) system. The consistency of the proposed tracking controller is established through ordinary differential equation theory. We conduct a series of simulations, and the results demonstrate the effectiveness and advantages of our higher-order tracking controller based on the multiple ZNN model with time delay in managing the tracking control challenges of the WAMV-VMD system.