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Communication-aware Multi-agent Systems Control Based on $k$-hop Distributed Observers

Tommaso Zaccherini, Siyuan Liu, Dimos V. Dimarogonas

TL;DR

It is demonstrated that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.

Abstract

We propose a distributed control strategy to allow the control of a multi-agent system requiring k-hop interactions based on the design of distributed state and input observers. In particular, we design for each agent a finite time convergent state and input observer that exploits only the communication with the 1-hop neighbors to reconstruct the information regarding those agents at a 2-hop distance or more. We then demonstrate that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.

Communication-aware Multi-agent Systems Control Based on $k$-hop Distributed Observers

TL;DR

It is demonstrated that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.

Abstract

We propose a distributed control strategy to allow the control of a multi-agent system requiring k-hop interactions based on the design of distributed state and input observers. In particular, we design for each agent a finite time convergent state and input observer that exploits only the communication with the 1-hop neighbors to reconstruct the information regarding those agents at a 2-hop distance or more. We then demonstrate that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.

Paper Structure

This paper contains 7 sections, 9 theorems, 44 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem setting
  3. Distributed -hop State Observer
  4. Distributed -hop Input Observer
  5. -hop Estimation-Based Feedback Controller
  6. Simulations
  7. Conclusion and Future Work

Key Result

Lemma 1

Consider an undirected graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$. If $\mathcal{G}$ is connected, then for all $j \in \mathcal{V}$ and all $i \in \mathcal{N}_{j}^{{k}\text{-hop}}$, $|\mathcal{N}_{i}^{{}}\cap \mathcal{N}_{j}^{{k}\text{-hop}}|> 0 \ \text{ or } \ |\mathcal{N}_{i}^{{}}\cap \mathcal{ Furthermore for all $j \in \mathcal{V}$ and for each connected component in the sub-graph $G_j = \{

Figures (2)

  • Figure 1: Graph $\mathcal{G}_T$ used for consensus.
  • Figure 2: Simulation results with $\pi_1= \pi_4= 9.7$, $\pi_2= \pi_3 =1.0$ as designed parameters for the input observer in \ref{['Eq: Input observer dynamic']}.

Theorems & Definitions (22)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 2
  • Theorem 1
  • proof
  • ...and 12 more