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Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking Control under Switching Topologies

Zewen Yang, Songbo Dong, Armin Lederer, Xiaobing Dai, Siyu Chen, Stefan Sosnowski, Georges Hattab, Sandra Hirche

TL;DR

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 that leverages a correlation-aware cooperative al- algorithm framework built upon Gaussian process regression.

Abstract

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.

Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking Control under Switching Topologies

TL;DR

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 that leverages a correlation-aware cooperative al- algorithm framework built upon Gaussian process regression.

Abstract

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.
Paper Structure (11 sections, 2 theorems, 42 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 2 theorems, 42 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Notation and Graph Theory
  4. Stochastic Communication Topology
  5. Euler-Lagrange Multi-agent System
  6. Distributed Learning with GPs
  7. Individual Learning
  8. Cooperative Learning with Correlation-Aware GPs
  9. Consensus Tracking under Switching Topology
  10. Simulation
  11. Conclusion

Key Result

Lemma 1

For a compact set for $\bm{p}$ as $\Omega \in \mathbb{R}^m$, consider the unknown function $\bm{f}(\cdot)$ in dyn_agent satisfying ass_f and GPs with the training data set ${\mathcal{D}}_i$ satisfying ass_data, $\forall i = 1,2,\dots,n$. Pick $\tau\in\mathbb{R}_+$, $\delta\in(0,1)$ such that $\min_{ for $r_{\Omega}=\max_{\bm{p},\bm{p}'\in\Omega}\|\bm{p}-\bm{p}'\|$, $L_{\mu_{ij}}$ and $L_{\sigma_{i

Figures (4)

  • Figure 1: (a) Switching communication topologies; (b) The agent $i$ has the data set $\mathcal{D}_i$. Meanwhile, the leader's trajectory $\bm{f}_r(t)$ crosses the whole data area.
  • Figure 2: Switching states.
  • Figure 3: Tracking error plots for the simulated scenarios.
  • Figure 4: The mean tracking error of different approaches.

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Theorem 1
  • proof