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Scale-free Non-collaborative Linear Protocol Design for A Class of Homogeneous Multi-agent Systems

Zhenwei Liu, Ali Saberi, Anton A. Stoorvogel

TL;DR

This work develops scale-free, non-collaborative linear protocols for achieving global state synchronization in homogeneous multi-agent systems, valid for both continuous- and discrete-time agents. It identifies necessary solvability conditions for the agent models and then provides complete design procedures: a two-stage approach for partial-state coupling that uses a left-invertible pre-compensator plus a Special Coordinate Basis, and static protocols for full-state coupling; in the discrete-time setting, a CSS observer-based scheme yields a scalable solution as well. The key contributions include explicit conditions that are nearly necessary, a full protocol design that is graph-size agnostic (requiring only a spanning tree), and numerical demonstrations on directed graphs showing effective scale-free synchronization without localized collaboration. The results have practical impact for large-scale MAS where network knowledge is limited, enabling robust and scalable coordination in settings ranging from passive to passifiable agent models.

Abstract

In this paper, we have focused on identifying a class of continuous- and discrete-time MAS for which a scale-free non-collaborative (i.e., scale-free fully distributed) linear protocol design is developed. We have identified conditions on agent models that enable us to design scalable linear protocols. Moreover, we show that these conditions are necessary if the agents are single input and single output. We also provide a complete design of scalable protocols for this class.

Scale-free Non-collaborative Linear Protocol Design for A Class of Homogeneous Multi-agent Systems

TL;DR

This work develops scale-free, non-collaborative linear protocols for achieving global state synchronization in homogeneous multi-agent systems, valid for both continuous- and discrete-time agents. It identifies necessary solvability conditions for the agent models and then provides complete design procedures: a two-stage approach for partial-state coupling that uses a left-invertible pre-compensator plus a Special Coordinate Basis, and static protocols for full-state coupling; in the discrete-time setting, a CSS observer-based scheme yields a scalable solution as well. The key contributions include explicit conditions that are nearly necessary, a full protocol design that is graph-size agnostic (requiring only a spanning tree), and numerical demonstrations on directed graphs showing effective scale-free synchronization without localized collaboration. The results have practical impact for large-scale MAS where network knowledge is limited, enabling robust and scalable coordination in settings ranging from passive to passifiable agent models.

Abstract

In this paper, we have focused on identifying a class of continuous- and discrete-time MAS for which a scale-free non-collaborative (i.e., scale-free fully distributed) linear protocol design is developed. We have identified conditions on agent models that enable us to design scalable linear protocols. Moreover, we show that these conditions are necessary if the agents are single input and single output. We also provide a complete design of scalable protocols for this class.
Paper Structure (13 sections, 7 theorems, 71 equations, 7 figures)

This paper contains 13 sections, 7 theorems, 71 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Necessary conditions for solvability
  4. Scale-free non-collaborative protocol design: Continuous-time case
  5. Protocol design for partial-state coupling
  6. Protocol design for full-state coupling, i.e. $C=I$
  7. Scale-free non-collaborative protocol design: Discrete-time case
  8. Protocol design for partial-state coupling
  9. Protocol design for full-state coupling, i.e. $C=I$
  10. Numerical Examples
  11. Continuous-time MAS
  12. Discrete-time MAS
  13. Conclusion

Key Result

Theorem 1

Consider a continuous-time, single-input, single-output MAS homo_sys with communication via zeta. There exists a linear protocol of the form protoco1 which achieves scale-free state synchronization problem without localized collaborative information exchange only if:

Figures (7)

  • Figure 1: Architecture of the scalable non-collaborative linear protocol
  • Figure 2: The compensated agent with pre-compensator
  • Figure 3: Directed topology network with $4$ nodes
  • Figure 4: State synchronization for continuous-time MAS with communication graph in Case $I$.
  • Figure 5: State synchronization for continuous-time MAS with communication graph in Case $II$.
  • ...and 2 more figures

Theorems & Definitions (12)

  • Definition 1
  • Remark 1
  • Theorem 1: Continuous-time MAS
  • Theorem 2: Discrete-time MAS
  • Remark 2
  • Lemma 1
  • Theorem 3
  • Theorem 4
  • Remark 3
  • Theorem 5
  • ...and 2 more