Machine learning is now widely applied across various domains, including industry, engineering, and research. While numerous mature machine learning models have been open-sourced on platforms like GitHub, their deployment often requires writing scripts in specific programming languages, such as Python, C++, or MATLAB. This dependency on particular languages creates a barrier for professionals outside the field of machine learning, making it challenging to integrate these algorithms into their workflows. To address this limitation, we propose GPgym in [1, 2], a remote service node based on Gaussian process regression. GPgym enables experts from diverse fields to seamlessly and flexibly incorporate machine learning techniques into their existing specialized software, without needing to write or manage complex script code.

Additionally, the investigation into the nested pointwise aggregation of In the realm of real-time online Gaussian Process (GP) experts has been undertaken [20], [21]. Nevertheless, the regression, continuously collecting the training data becomes application of pointwise aggregation across the entirety of impractical for dynamic systems due to the constraints in the training dataset proves unattainable within distributed physical storage space and the escalating computational burden systems. Instead of employing the entire dataset for prediction, poses substantial practical challenges, particularly in real-time several approximation techniques prove instrumental. Moreover, local approximation B. Agent-based Gaussian Process methods, such as the naive local experts, the mixture of Distributed learning finds prominent application in multiagent experts, and the product of experts, present viable alternatives. Consequently, joint predictions are aggregated [8]. Several efforts have been dedicated to implementing distributed Prominently, cooperative learning within distributed systems Gaussian Process (DGP) methodologies within MASs.

Consensus control in multi-agent systems has received significant attention and practical implementation across various domains. However, managing consensus control under unknown dynamics remains a significant challenge for control design due to system uncertainties and environmental disturbances. This paper presents a novel learning-based distributed control law, augmented by an auxiliary dynamics. Gaussian processes are harnessed to compensate for the unknown components of the multi-agent system. For continuous enhancement in predictive performance of Gaussian process model, a data-efficient online learning strategy with a decentralized event-triggered mechanism is proposed. Furthermore, the control performance of the proposed approach is ensured via the Lyapunov theory, based on a probabilistic guarantee for prediction error bounds. To demonstrate the efficacy of the proposed learning-based controller, a comparative analysis is conducted, contrasting it with both conventional distributed control laws and offline learning methodologies.

This work presents an innovative learning-based approach to tackle the tracking control problem of Euler-Lagrange multi-agent systems with partially unknown dynamics operating under switching communication topologies. The approach leverages a correlation-aware cooperative algorithm framework built upon Gaussian process regression, which adeptly captures inter-agent correlations for uncertainty predictions. A standout feature is its exceptional efficiency in deriving the aggregation weights achieved by circumventing the computationally intensive posterior variance calculations. Through Lyapunov stability analysis, the distributed control law ensures bounded tracking errors with high probability. Simulation experiments validate the protocol's efficacy in effectively managing complex scenarios, establishing it as a promising solution for robust tracking control in multi-agent systems characterized by uncertain dynamics and dynamic communication structures.

This paper introduces an innovative approach to enhance distributed cooperative learning using Gaussian process (GP) regression in multi-agent systems (MASs). The key contribution of this work is the development of an elective learning algorithm, namely prior-aware elective distributed GP (Pri-GP), which empowers agents with the capability to selectively request predictions from neighboring agents based on their trustworthiness. The proposed Pri-GP effectively improves individual prediction accuracy, especially in cases where the prior knowledge of an agent is incorrect. Moreover, it eliminates the need for computationally intensive variance calculations for determining aggregation weights in distributed GP. Furthermore, we establish a prediction error bound within the Pri-GP framework, ensuring the reliability of predictions, which is regarded as a crucial property in safety-critical MAS applications.

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.

When the dynamics of systems are unknown, supervised machine learning techniques are commonly employed to infer models from data. Gaussian process (GP) regression is a particularly popular learning method for this purpose due to the existence of prediction error bounds. Moreover, GP models can be efficiently updated online, such that event-triggered online learning strategies can be pursued to ensure specified tracking accuracies. However, existing trigger conditions must be able to be evaluated at arbitrary times, which cannot be achieved in practice due to non-negligible computation times. Therefore, we first derive a delay-aware tracking error bound, which reveals an accuracy-delay trade-off. Based on this result, we propose a novel event trigger for GP-based online learning with computational delays, which we show to offer advantages over offline trained GP models for sufficiently small computation times. Finally, we demonstrate the effectiveness of the proposed event trigger for online learning in simulations.