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.

利用高斯过程学习补偿多智能体系统中未知的组成部分，并通过基于概率保证的预测误差边界确保了所提出的基于学习的控制器的控制性能。

基于高斯过程回归的分布式事件触发在线学习，用于多智能体系统的安全共识

Decentralized Event-Triggered Online Learning for Safe Consensus of  Multi-Agent Systems with Gaussian Process Regression

This paper studies the algorithmic stability and generalizability of
decentralized stochastic gradient descent (D-SGD). We prove that the consensus
model learned by D-SGD is $\mathcal{O}{(N^{-1}+m^{-1} +\lambda^2)}$-stable in
expectation in the non-convex non-smooth setting, where $N$ is the total sample
size, $m$ is the worker number, and $1+\lambda$ is the spectral gap that
measures the connectivity of the communication topology. These results then
deliver an $\mathcal{O}{(N^{-(1+\alpha)/2}+
m^{-(1+\alpha)/2}+\lambda^{1+\alpha} + \phi_{\mathcal{S}})}$ in-average
generalization bound, which is non-vacuous even when $\lambda$ is closed to
$1$, in contrast to vacuous as suggested by existing literature on the
projected version of D-SGD. Our theory indicates that the generalizability of
D-SGD is positively correlated with the spectral gap, and can explain why
consensus control in initial training phase can ensure better generalization.
Experiments of VGG-11 and ResNet-18 on CIFAR-10, CIFAR-100 and Tiny-ImageNet
justify our theory. To our best knowledge, this is the first work on the
topology-aware generalization of vanilla D-SGD. Code is available at
this https URL

研究了分散随机梯度下降（D-SGD）算法的算法稳定性和分布特性，证明了 D-SGD 认为的共识模型具有稳定性，证明了 D-SGD 具有一般化的可行性。D-SGD 的可行性与谱间隙呈正相关，并且可以解释为什么最初的培训阶段的共识控制可以确保更好的一般化，这是 vanilla-D-SGD 的拓扑感知广义性的第一个工作。

拓扑感知的去中心化 SGD 的泛化

Topology-aware Generalization of Decentralized SGD

We study the numerical realisation of optimal consensus control laws for
agent-based models. For a nonlinear multi-agent system of Cucker-Smale type,
consensus control is cast as a dynamic optimisation problem for which we derive
first-order necessary optimality conditions. In the case of a smooth
penalization fo the control energy, the optimality system is numerically
approximated via a gradient-descent method. For sparsity promoting, non-smooth
$\ell_1$-norm control penalizations, the optimal controllers are realised by
means of heuristic methods. For an increasing number of agents, we discuss the
approximation of the consensus control problem by following a mean-field
modelling approach.

研究使用优化方法实现共识控制算法，采用梯度下降方法实现平滑控制势能的最优控制器，采用启发式方法实现促进稀疏性的非平滑控制 L1 范数的最优控制器，对于非线性多代理机制的 Cucker-Smale 类型，采用平均场建模进行问题逼近。