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Robust Integral Consensus Control of Multi-Agent Networks Perturbed by Matched and Unmatched Disturbances: The Case of Directed Graphs

Jose Guadalupe Romero, David Navarro-Alarcon

TL;DR

A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented and a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree is presented.

Abstract

This work presents a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree. We propose new robust controllers to solve the consensus and synchronization problems when the systems are under the effects of matched and unmatched disturbances. In both problems, we present simple continuous controllers, whose integral actions allow us to handle the disturbances. A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented. To assess the performance of our result, a representative simulation study is presented.

Robust Integral Consensus Control of Multi-Agent Networks Perturbed by Matched and Unmatched Disturbances: The Case of Directed Graphs

TL;DR

A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented and a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree is presented.

Abstract

This work presents a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree. We propose new robust controllers to solve the consensus and synchronization problems when the systems are under the effects of matched and unmatched disturbances. In both problems, we present simple continuous controllers, whose integral actions allow us to handle the disturbances. A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented. To assess the performance of our result, a representative simulation study is presented.
Paper Structure (7 sections, 6 theorems, 50 equations, 11 figures)

This paper contains 7 sections, 6 theorems, 50 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Notation.
  3. Problem Formulation
  4. Problem statement.
  5. Main Result
  6. Simulations
  7. Conclusions

Key Result

Lemma 1

RENBEARD The Laplacian matrix $L$ has a unique zero-eigenvalue and, by construction, the rest of its spectrum is strictly positive and satisfies $L \boldsymbol 1_N = 0$, with $\boldsymbol 1_N \in \mathbb{R}^N$ as its associated right eigenvector.

Figures (11)

  • Figure 1: A spanning-tree graph and its corresponding Laplacian
  • Figure 2: Transient behavior of $e_{\star_i}$ with $i:1:5$
  • Figure 3: Transient behavior of $x_i$ with $i:1:5$
  • Figure 4: Transient behavior of $y_i$ with $i:1:5$
  • Figure 5: Transient behavior of the integral action $\hat{\delta}_i$ with $i:1:5$
  • ...and 6 more figures

Theorems & Definitions (15)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • proof
  • Corollary 1
  • proof
  • Proposition 2
  • proof
  • Corollary 2
  • proof
  • ...and 5 more