This paper investigates the issue of finite-time cooperative depth control of a multi-autonomous underwater vehicle (AUV) system with heterogeneous dynamical structures and heterogeneous time-varying parameters. Initially, we introduce a hierarchical control architecture to decouple communication from the local dynamics effectively, thus mitigating the complexities introduced by such heterogeneity. The architecture leverages the Internal Model Principle (IMP) to transform the arduous task of finite-time cooperative depth control for the heterogeneous multi-AUV system into tractable individual finite-time observation and tracking problems, which simplifies the overall control problem substantially. Subsequently, in response to both finite-time observing and tracking problems, a cooperative observer is designed based on a potential function, and a distributed local feedback controller is developed to achieve finite-time cooperative control. Stability parameter conditions for both the observer and controller are derived rigorously to facilitate control design. The proposed control approach relaxes the constraints on communication topology and dynamics, enhancing its practical applicability in multi-AUV systems. The feasibility of the hierarchical architecture and the finite-time stability of the upper observer and lower controller are rigorously analyzed. Comparative numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed methods.

A hierarchical framework for finite-time cooperative depth control of heterogeneous multi-AUV system