For single agent systems, probabilistic machine learning techniques such as Gaussian process regression have been shown to be suitable methods for inferring models of unknown nonlinearities, which can be employed to improve the performance of control laws. While this approach can be extended to the cooperative control of multiagent systems, it leads to a decentralized learning of the unknown nonlinearity, i.e., each agent independently infers a model. However, decentralized learning can potentially lead to poor control performance, since the models of individual agents are often accurate in merely a small region of the state space. In order to overcome this issue, we propose a novel method for the distributed aggregation of Gaussian process models, and extend probabilistic error bounds for Gaussian process regression to the proposed approach. Based on this distributed learning method, we develop a cooperative tracking control law for leader–follower consensus of multiagent systems with partially unknown, higher order, control-affine dynamics, and analyze its stability using the Lyapunov theory. The effectiveness of the proposed methods is demonstrated in numerical evaluations.

Considering the actual situation of time-varying interference in the underwater environment, a trajectory tracking control method for an underactuated Unmanned Underwater Vehicle (UUV) underwater exploration based on backstepping sliding mode with fuzzy switching gain is designed in this paper. Firstly, the motion equations of UUV in diving plane are given. Secondly, the virtual control variable is designed to replace the pitch angle to avoid the singular value phenomenon. Combining with the backstepping technique, the fuzzy switching sliding mode controller is proposed. Thirdly, in order to decrease the chattering phenomenon of sliding mode control, the fuzzy rule of sliding mode gain is designed. Fourthly, based on Lyapunov theory and comparison principle, the global asymptotic stability of UUV closed-loop tracking error system is proved. Finally, the simulation results demonstrate the effectiveness and robustness of the proposed controller.

To solve the navigation accuracy problems of multi-Unmanned Underwater Vehicles (multi-UUVs) in the polar region, a polar cooperative navigation algorithm for multi-UUVs considering communication delays is proposed in this paper. UUVs are important pieces of equipment in ocean engineering for marine development. For UUVs to complete missions, precise navigation is necessary. It is difficult for UUVs to establish true headings because of the rapid convergence of Earth meridians and the severe polar environment. Based on the polar grid navigation algorithm, UUV navigation in the polar region can be accomplished with the Strapdown Inertial Navigation System (SINS) in the grid frame. To save costs, a leader-follower type of system is introduced in this paper. The leader UUV helps the follower UUVs to achieve high navigation accuracy. Follower UUVs correct their own states based on the information sent by the leader UUV and the relative position measured by ultra-short baseline (USBL) acoustic positioning. The underwater acoustic communication delay is quantized by the model. In this paper, considering underwater acoustic communication delay, the conventional adaptive Kalman filter (AKF) is modified to adapt to polar cooperative navigation. The results demonstrate that the polar cooperative navigation algorithm for multi-UUVs that considers communication delays can effectively navigate the sailing of multi-UUVs in the polar region.

In the realm of the cooperative control of multiagent systems (MASs) with unknown dynamics, Gaussian process (GP) regression is widely used to infer the uncertainties due to its modeling flexibility of nonlinear functions and the existence of a theoretical prediction error bound. Online learning, which involves incorporating newly acquired training data into GP models, promises to improve control performance by enhancing predictions during the operation. Therefore, this article investigates the online cooperative learning algorithm for MAS control. Moreover, an event-triggered data selection mechanism, inspired by the analysis of a centralized event-trigger (CET), is introduced to reduce the model update frequency and enhance the data efficiency. With the proposed learning-based control, the practical convergence of the MAS is validated with guaranteed tracking performance via the Lyapunov theory. Furthermore, the exclusion of the Zeno behavior for individual agents is shown. Finally, the effectiveness of the proposed event-triggered online learning method is demonstrated in simulations.