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Consensus in Plug-and-Play Heterogeneous Dynamical Networks: A Passivity Compensation Approach

Yongkang Su, Sei Zhen Khong, Lanlan Su

Abstract

This paper investigates output consensus in heterogeneous dynamical networks within a plug-and-play framework. The networks are interconnected through nonlinear diffusive couplings and operate in the presence of measurement and communication noise. Focusing on systems that are input feedforward passive (IFP), we propose a passivity-compensation approach that exploits the surplus passivity of coupling links to locally offset shortages of passivity at the nodes. This mechanism enables subnetworks to be interconnected without requiring global reanalysis, thereby preserving modularity. Specifically, we derive locally verifiable interface conditions, expressed in terms of passivity indices and coupling gains, to guarantee that consensus properties of individual subnetworks are preserved when forming larger networks.

Consensus in Plug-and-Play Heterogeneous Dynamical Networks: A Passivity Compensation Approach

Abstract

This paper investigates output consensus in heterogeneous dynamical networks within a plug-and-play framework. The networks are interconnected through nonlinear diffusive couplings and operate in the presence of measurement and communication noise. Focusing on systems that are input feedforward passive (IFP), we propose a passivity-compensation approach that exploits the surplus passivity of coupling links to locally offset shortages of passivity at the nodes. This mechanism enables subnetworks to be interconnected without requiring global reanalysis, thereby preserving modularity. Specifically, we derive locally verifiable interface conditions, expressed in terms of passivity indices and coupling gains, to guarantee that consensus properties of individual subnetworks are preserved when forming larger networks.
Paper Structure (8 sections, 3 theorems, 31 equations, 4 figures)

This paper contains 8 sections, 3 theorems, 31 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Problem description
  4. Main Results
  5. Single-node plug-and-play consensus
  6. Network plug-and-play consensus
  7. Numerical Example
  8. Conclusion

Key Result

Lemma 1

Given an undirected and connected graph $\mathcal{G} = (\mathcal{N}, \mathcal{E})$, let $D\in\mathbb{R}^{n\times p}$ be its incident matrix, and let $\Theta =\mathrm{diag}\{\theta_1,\ldots,\theta_n\}$ and $\Sigma =\mathrm{diag}\{\sigma_1,\ldots,\sigma_p\}$. It holds that if there exists a diagonal matrix $S=\mathrm{diag}\left\{ {{s _1}, \ldots, s_p} \right\}\succ 0$ such that for each edge $\left

Figures (4)

  • Figure 1: Block diagram of the network \ref{['eq: system model']} and \ref{['eq: input']}.
  • Figure 2: Illustration of the interconnection assumption between two connected graphs $\mathcal{G}_1$ and $\mathcal{G}_2$.
  • Figure 3: The networks considered in the Example.
  • Figure 4: Output trajectories of the systems in the Example.

Theorems & Definitions (8)

  • Definition 1: DesVid75
  • Lemma 1
  • Definition 2
  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof