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

TL;DR

The paper tackles average consensus in multi-agent systems with unknown dynamics by integrating a distributed controller with an auxiliary dynamics and Gaussian Process-based online learning to compensate the unknown term $f(\cdot)$. It introduces a decentralized event-triggered mechanism that selectively augments the GP training data, yielding probabilistic bounds on prediction errors and stability via a Lyapunov framework. The main theoretical result proves a probabilistic $\epsilon$-average consensus with $\epsilon = 2 c^{-1} N \underline{\eta}$ and high-confidence guarantees, while simulations and Monte Carlo tests show improved performance and data efficiency over offline learning. The approach offers a safe, scalable solution for learning-based coordination in MAS under uncertainties, with tunable speed and accuracy through separate control gains and learning parameters.

Abstract

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.

Figures (4)

• Figure 1: The average state $\bar{x}^*$ and the actual state $x_i$ for each agent over time using different controllers and learning strategies, which are corresponding to the $4$ cases in \ref{['subsection_simulation_setting']}.
• Figure 2: The value of trigger function $\rho(x_i, \bar{x}_i)$ and the time of the trigger events for each agent $i \in \mathcal{V}$ for case (d).
• Figure 3: Average consensus error over time with variance.
• Figure 4: Maximal size of data set, which for offline learning in cases (a) and (c) is $150$ from the size of initial data set. With naive event-triggered online learning \ref{['eqn_naive_trigger_function']} in case (b), the maximal size of the data set for each agent $1$ to $4$ denotes $104 \pm 42$, $98 \pm 43$, $108 \pm 42$ and $104 \pm 43$, respectively. The maximal numbers of training samples in case (d) collected through decentralized event-triggered mechanism with \ref{['eqn_trigger_function']} are $102 \pm 41$, $97 \pm 42$, $107 \pm 41$ and $102 \pm 42$ for agent $1$ to $4$, respectively.

Theorems & Definitions (2)

• proof
• proof