Hierarchical fully distributed optimal formation tracking control for USVs with wave disturbances under input saturation

This paper investigates fully distributed optimal formation tracking problems for multi-USV (Unmanned Surface Vehicle) systems subject to wave disturbances and input saturation. A hierarchical control framework is proposed, where the planning layer employs a primal-dual algorithm to design distributed generators that minimize the sum of local cost functions, while ensuring all trajectories achieve consensus. In the control layer, a fuzzy distributed formation tracking protocol with adaptive coupling gains is devised to maintain the formation structure, and track the optimal formation center signal from the planning layer. Both layers are designed independently of the global Laplacian matrix information. Furthermore, due to the limited actual output power of the actuators, a hyperbolic tangent function is introduced to model input saturation of USVs, and based on the dynamic surface control method, an augmented state is constructed to transform the system into a non-saturation condition. By combining Lyapunov theory with random differential equations, the mean square of formation tracking errors for multi-USV systems with non-white noise is proved to be bounded. Finally, numerical simulations validate the effectiveness of the proposed algorithms.