Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Data-Driven Cooperative Output Regulation of Continuous-Time Multi-Agent Systems with Unknown Network Topology

Peng Ren, Yuqing Hao, Zhiyong Sun, Qingyun Wang, Guanrong Chen

TL;DR

The paper develops a data-driven approach for cooperative output regulation of continuous-time multi-agent systems with unknown network topology. It leverages an orthogonal polynomial basis to process data without state-derivative measurements and derives a data-informativity framework that yields necessary and sufficient conditions for exact data and robust bounds under noise. A topology-agnostic design uses a lower bound on the Laplacian's minimum nonzero eigenvalue, computed from edge-weight bounds, to ensure stability of the communication-partnered dynamics, while regulator equations guide distributed gain computation. The results are validated via numerical simulations showing convergence under exact data and bounded tracking error under noisy data, including topology switching scenarios. This contributes a practical, topology-agnostic, data-driven pathway for distributed control in networks with uncertain interconnections and data quality.

Abstract

This paper investigates data-driven cooperative output regulation for continuous-time multi-agent systems with unknown network topology. Unlike existing studies that typically assume a known network topology to directly compute controller parameters, a novel approach is proposed that allows for the computation of the parameter without prior knowledge of the topology. A lower bound on the minimum non-zero eigenvalue of the Laplacian matrix is estimated using only edge weight bounds, enabling the output regulation controller design to be independent of global network information. Additionally, the common need for state derivative measurements is eliminated, reducing the amount of data requirements. Furthermore, necessary and sufficient conditions are established to ensure that the data are informative for cooperative output regulation, leading to the design of a distributed output regulation controller. For the case with noisy data, the bound of the output error is provided, which is positively correlated with the noise bound, and a distributed controller is constructed for the approximate cooperative output regulation. Finally, the effectiveness of the proposed methods is verified through numerical simulations.

Data-Driven Cooperative Output Regulation of Continuous-Time Multi-Agent Systems with Unknown Network Topology

TL;DR

The paper develops a data-driven approach for cooperative output regulation of continuous-time multi-agent systems with unknown network topology. It leverages an orthogonal polynomial basis to process data without state-derivative measurements and derives a data-informativity framework that yields necessary and sufficient conditions for exact data and robust bounds under noise. A topology-agnostic design uses a lower bound on the Laplacian's minimum nonzero eigenvalue, computed from edge-weight bounds, to ensure stability of the communication-partnered dynamics, while regulator equations guide distributed gain computation. The results are validated via numerical simulations showing convergence under exact data and bounded tracking error under noisy data, including topology switching scenarios. This contributes a practical, topology-agnostic, data-driven pathway for distributed control in networks with uncertain interconnections and data quality.

Abstract

This paper investigates data-driven cooperative output regulation for continuous-time multi-agent systems with unknown network topology. Unlike existing studies that typically assume a known network topology to directly compute controller parameters, a novel approach is proposed that allows for the computation of the parameter without prior knowledge of the topology. A lower bound on the minimum non-zero eigenvalue of the Laplacian matrix is estimated using only edge weight bounds, enabling the output regulation controller design to be independent of global network information. Additionally, the common need for state derivative measurements is eliminated, reducing the amount of data requirements. Furthermore, necessary and sufficient conditions are established to ensure that the data are informative for cooperative output regulation, leading to the design of a distributed output regulation controller. For the case with noisy data, the bound of the output error is provided, which is positively correlated with the noise bound, and a distributed controller is constructed for the approximate cooperative output regulation. Finally, the effectiveness of the proposed methods is verified through numerical simulations.
Paper Structure (14 sections, 15 theorems, 99 equations, 8 figures, 3 tables, 1 algorithm)

This paper contains 14 sections, 15 theorems, 99 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. PRELIMINARIES
  3. Notation
  4. Graph Theory
  5. Orthogonal Polynomial Basis
  6. PROBLEM FORMULATION
  7. MAIN RESULT
  8. Exact data case
  9. The stabilizability of $A_C$
  10. Unkown network topology
  11. The cooperative output regulation
  12. Noisy data case
  13. NUMERICAL SIMULATION
  14. CONCLUSION

Key Result

Lemma 1

(see trefethen2019approximation) Let $\{C_{k}\}_{k \in \mathbb{N}}$ be the Chebyshev basis, and $f \in \mathcal{L}_{2}(\mathbb{I},\mathbb{R})$ with $N \in \mathbb{N}$ and $N \geq 1$. Suppose that $f$, $f^{(1)}$ are absolutely continuous, and that $V(f^{(2)})=\left \| \frac{d^{2}f}{d^{2}t} \right \|_

Figures (8)

  • Figure 1: Followers are connected on different graphs.
  • Figure 2: Leader connects to all followers and followers are connected by an undirected graph.
  • Figure 3: Network topology for the graph $\mathcal{G}_{1}$
  • Figure 4: Tracking errors of the followers using exact data.
  • Figure 5: Switching network topology from $\mathcal{G}_{2}$ to $\mathcal{G}_{3}$.
  • ...and 3 more figures

Theorems & Definitions (38)

  • Lemma 1
  • Remark 1
  • Definition 1
  • Lemma 2
  • Lemma 3
  • Remark 2
  • Definition 2
  • Lemma 4
  • Theorem 1
  • proof
  • ...and 28 more