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Cooperative Online Learning for Multi-Agent System Control via Gaussian Processes with Event-Triggered Mechanism: Extended Version

Xiaobing Dai, Zewen Yang, Sihua Zhang, Di-Hua Zhai, Yuanqing Xia, Sandra Hirche

TL;DR

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 and the effectiveness of the proposed event-triggered online learning method is demonstrated in simulations.

Abstract

In the realm of the cooperative control of multi-agent 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 Gaussian process models, promises to improve control performance by enhancing predictions during the operation. Therefore, this paper 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, 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 Lynaponve 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.

Cooperative Online Learning for Multi-Agent System Control via Gaussian Processes with Event-Triggered Mechanism: Extended Version

TL;DR

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 and the effectiveness of the proposed event-triggered online learning method is demonstrated in simulations.

Abstract

In the realm of the cooperative control of multi-agent 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 Gaussian process models, promises to improve control performance by enhancing predictions during the operation. Therefore, this paper 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, 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 Lynaponve 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.
Paper Structure (23 sections, 13 theorems, 99 equations, 13 figures)

This paper contains 23 sections, 13 theorems, 99 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Contribution and Structure
  3. Notation and Graph Theory
  4. Problem Setting and Preliminaries
  5. Multi-Agent System
  6. Distributed Control Law
  7. Cooperative Online Learning based Distributed Control with Gaussian Processes
  8. Gaussian Process Regression
  9. Cooperative Online Learning
  10. Control Performance Analysis
  11. Event-triggered Online Learning
  12. Centralized Event-triggered Online Learning
  13. Distributed Event-triggered Online Learning
  14. Zeno Behavior for Event-triggered Cooperative Learning
  15. Numerical Simulations
  16. ...and 8 more sections

Key Result

Lemma 1

Suppose assumption_topology holds and choose $\bm{q} \in \mathbb{R}^N$ and $\bm{P} \in \mathbb{R}^{N \times N}$ defined as Let $\bm{Q} = \bm{P} (\bm{\mathcal{L}} + \bm{\mathcal{B}}) + (\bm{\mathcal{L}} + \bm{\mathcal{B}})^T \bm{P} \in \mathbb{R}^{N \times N}$, then the matrices $\bm{P}$ and $\bm{Q}$ are symmetric positive definite.

Figures (13)

  • Figure 1: (a) Communication topology among agents and leader; (b) The manifold of the unknown function $f(\cdot)$ evaluated on the compact domain $\mathbb{X}$.
  • Figure 2: Uniformly distributed initial data set for offline learning for instance at agent $1$ and the references, including the trajectory for leader $\bm{x}_l$ and $\bm{x}_l + \bm{s}_i$ for each agent $i \in \mathcal{V}$.
  • Figure 3: System states and tracking error of each agent over time.
  • Figure 4: Overall tracking error with respect to time.
  • Figure 5: Trigger times and instances for centralized and distributed event-trigger mechanisms for each agent. Specifically, for centralized version $131$, $130$, $122$ and $120$ samples are collected for agent $1$ to $4$. The minimal trigger interval for each agent denotes $0.036$, $0.027$, $0.020$ and $0.020$. With distributed event-trigger, each agent collects $154$, $150$, $132$ and $131$ data pairs under minimal trigger interval $0.025$, $0.024$, $0.016$ and $0.021$.
  • ...and 8 more figures

Theorems & Definitions (20)

  • Lemma 1: $\!\!$zhang2012adaptive
  • Lemma 2: $\!\!$ lederer2019uniform
  • Lemma 3
  • Corollary 1
  • Remark 1
  • Corollary 2
  • Lemma 4
  • Theorem 1
  • Proposition 1
  • Remark 2
  • ...and 10 more