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Scalable δ-Level Coherent State Synchronization of Multi-Agent Systems in the Presence of Bounded Disturbances

Donya Nojavanzadeh, Zhenwei Liu, Ali Saberi, Anton A. Stoorvogel

TL;DR

A scale-free framework designed solely based on the knowledge of agent models and agnostic to the communication graph and the size of the network to restrict the network's coherency level to $\delta$ without a-priori information about the disturbance.

Abstract

In this paper, we study scalable $δ-$level coherent state synchronization for multi-agent systems (MAS) where the agents are subject to bounded disturbances/noises. We propose a scale-free framework designed solely based on the knowledge of agent models and agnostic to the communication graph and the size of the network. We define the level of coherency for each agent as the norm of the weighted sum of the disagreement dynamics with its neighbors. The objective is to restrict the network's coherency level to $δ$ without a-priori information about the disturbance.

Scalable δ-Level Coherent State Synchronization of Multi-Agent Systems in the Presence of Bounded Disturbances

TL;DR

A scale-free framework designed solely based on the knowledge of agent models and agnostic to the communication graph and the size of the network to restrict the network's coherency level to without a-priori information about the disturbance.

Abstract

In this paper, we study scalable level coherent state synchronization for multi-agent systems (MAS) where the agents are subject to bounded disturbances/noises. We propose a scale-free framework designed solely based on the knowledge of agent models and agnostic to the communication graph and the size of the network. We define the level of coherency for each agent as the norm of the weighted sum of the disagreement dynamics with its neighbors. The objective is to restrict the network's coherency level to without a-priori information about the disturbance.
Paper Structure (14 sections, 7 theorems, 144 equations, 15 figures, 1 table)

This paper contains 14 sections, 7 theorems, 144 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Protocol design
  4. Numerical examples
  5. Scalability -- independence to the size of communication networks
  6. Directed graphs
  7. Undirected graphs
  8. Effectiveness with disconnected graphs
  9. Disconnected directed graphs
  10. Disconnected undirected graphs
  11. Effectiveness with different types of communication graphs
  12. Robustness to different noise patterns
  13. Effectiveness for different values of $\delta$.
  14. Conclusion

Key Result

Theorem 1

Consider a MAS agent-g-noise with associated network communication zetanoise and a given parameter $\delta>0$ satisfying Assumption ass. The scalable $\delta$-level-coherent state synchronization in the presence of bounded external disturbances/noises as stated in problem prob_x is solvable. In part

Figures (15)

  • Figure 1: Vicsek fractal graphs
  • Figure 2: Circulant graph
  • Figure 3: Disconnected directed graph
  • Figure 4: Disconnected undirected graph
  • Figure 5: $\delta$-level coherent state synchronization of MAS with directed Vicsek fractal communication graphs and $N=5$ in the presence of disturbances via protocol \ref{['protocol-example']} with $d=0.5$
  • ...and 10 more figures

Theorems & Definitions (11)

  • Definition 1
  • Remark 1
  • Definition 2
  • Theorem 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • ...and 1 more