Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating new data with polynomial-time computation, making them well-suited for safety-critical dynamical systems that require rapid adaptation. However, the inference and online updates of exact GPs, when processing streaming data, incur cubic computation time and quadratic storage memory complexity, limiting their scalability to large datasets in real-time settings. In this paper, we propose a streaming kernel-induced progressively generated expert framework of Gaussian processes (SkyGP) that addresses both computational and memory constraints by maintaining a bounded set of experts, while inheriting the learning performance guarantees from exact Gaussian processes. Furthermore, two SkyGP variants are introduced, each tailored to a specific objective, either maximizing prediction accuracy (SkyGP-Dense) or improving computational efficiency (SkyGP-Fast). The effectiveness of SkyGP is validated through extensive benchmarks and real-time control experiments demonstrating its superior performance compared to state-of-the-art approaches.

In this paper, we address a practical distributed Bayesian learning problem with asynchronous measurements and predictions due to diverse computational conditions. To this end, asynchronous distributed Gaussian process (AsyncDGP) regression is proposed, which is the first effective online distributed Gaussian processes (GPs) approach to improve the prediction accuracy in real-time learning tasks. By leveraging the devised evaluation criterion and established prediction error bounds, AsyncDGP enables the distinction of contributions of each model for prediction ensembling using aggregation strategy. Furthermore, we extend its utility to dynamic systems by introducing a learning-based control law, ensuring guaranteed control performance in safety-critical applications. Additionally, a networked online learning simulation platform for distributed GPs, namely online GP gym (GPgym), is introduced for testing the performance of learning and control of dynamical systems. Numerical simulations within GPgym across regression tasks with real-world data sets and dynamical control scenarios demonstrate the effectiveness and applicability of AsyncDGP.

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.

The growing demand for accurate control in varying and unknown environments has sparked a corresponding increase in the requirements for power supply components, including permanent magnet synchronous motors (PMSMs). To infer the unknown part of the system, machine learning techniques are widely employed, especially Gaussian process regression (GPR) due to its flexibility of continuous system modeling and its guaranteed performance. For practical implementation, distributed GPR is adopted to alleviate the high computational complexity. However, the study of distributed GPR from a control perspective remains an open problem. In this paper, a control-aware optimal aggregation strategy of distributed GPR for PMSMs is proposed based on the Lyapunov stability theory. This strategy exclusively leverages the posterior mean, thereby obviating the need for computationally intensive calculations associated with posterior variance in alternative approaches. Moreover, the straightforward calculation process of our proposed strategy lends itself to seamless implementation in high-frequency PMSM control. The effectiveness of the proposed strategy is demonstrated in the simulations.

Abstract This paper presents a whale optimization algorithm (WOA) based on forward looking sonar to achieve two‐dimensional optimal path planning for an autonomous underwater vehicle. The purpose of path planning is not only to effectively avoid threat regions and safely reach the intended target with minimum fuel cost but also to obtain an optimal or near‐optimal path in a complex ocean battlefield environment. The WOA, based on the bubble‐net attacking behavior of humpback whales, mimics encircling the prey, attacks with a bubble‐net method, and search for prey to effectively determine the global optimal solution in the search space. The WOA not only has fast convergence speed and high calculation accuracy but can also effectively balance exploration and exploitation to avoid falling into a local optimum and obtain the global optimal solution. Five sets of experiments are applied to verify the superiority and stability of the WOA. Compared with other algorithms, such as artificial bee colony, bat algorithm, cuckoo search, flower pollination algorithm, moth‐flame optimization algorithm, particle swarm optimization, and water wave optimization, the WOA exhibits better optimization performance and stronger robustness. The experimental results reveal that the WOA can find the shortest path compared with all the other algorithms, and it is an effective and feasible method for solving the path planning problem.

The multiple UUVs(unmanned underwater vehicles) can maintain a certain formation and complete the designated route cruise mission by using the path tracking controller. According to the problem of multiple UUV path tracking under discrete information conditions, a path tracking controller based on virtual leader is proposed in this paper considering communication delays. Firstly, the coupled nonlinear UUV kinematics and dynamics equations are transformed into second-order affine forms by using feedback linearization method, and the mathematical model under discrete time is given. Secondly, the path tracking controller is designed in the case of bounded time delays, and the sufficient conditions are analyzed and proposed based on the matrix theory. Finally, the effectiveness of the proposed algorithm is proved by the simulation experiments, all trajectories of each UUV converge to the desired trajectories under the specific formation.