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Distributed Finite-time Differentiator for Multi-agent Systems Under Directed Graph

Weile Chen, Haibo Du, Shihua Li

TL;DR

This work addresses distributed finite-time differentiation in multi-agent systems over directed graphs by introducing two variants of a distributed finite-time differentiator (DFD): one that uses relative position information and another that uses absolute position information. The authors prove finite-time stability via Lyapunov analysis and extend the differentiator to a continuous finite-time consensus controller for leader-follower MAS, achieving robust, chattering-free output consensus under disturbances. Through simulations, they demonstrate finite-time convergence of both the estimated leader signals and the follower outputs, validating the effectiveness of the DFD framework and the continuous controller. The contributions enable accurate distributed state estimation and finite-time synchronization in networks where global measurements or velocity sensing are unavailable, with potential applications in formation control and cooperative robotics.

Abstract

This paper proposes a new distributed finite-time differentiator (DFD) for multi-agent systems (MAS) under directed graph, which extends the differentiator algorithm from the centralized case to the distributed case by only using relative/absolute position information. By skillfully constructing a Lyapunov function, the finite-time stability of the closed-loop system under DFD is proved. Inspired by the duality principle of control theory, a distributed continuous finite-time output consensus algorithm extended from DFD for a class of leader-follower MAS is provided, which not only completely suppresses disturbance, but also avoids chattering. Finally, several simulation examples are given to verify the effectiveness of the DFD.

Distributed Finite-time Differentiator for Multi-agent Systems Under Directed Graph

TL;DR

This work addresses distributed finite-time differentiation in multi-agent systems over directed graphs by introducing two variants of a distributed finite-time differentiator (DFD): one that uses relative position information and another that uses absolute position information. The authors prove finite-time stability via Lyapunov analysis and extend the differentiator to a continuous finite-time consensus controller for leader-follower MAS, achieving robust, chattering-free output consensus under disturbances. Through simulations, they demonstrate finite-time convergence of both the estimated leader signals and the follower outputs, validating the effectiveness of the DFD framework and the continuous controller. The contributions enable accurate distributed state estimation and finite-time synchronization in networks where global measurements or velocity sensing are unavailable, with potential applications in formation control and cooperative robotics.

Abstract

This paper proposes a new distributed finite-time differentiator (DFD) for multi-agent systems (MAS) under directed graph, which extends the differentiator algorithm from the centralized case to the distributed case by only using relative/absolute position information. By skillfully constructing a Lyapunov function, the finite-time stability of the closed-loop system under DFD is proved. Inspired by the duality principle of control theory, a distributed continuous finite-time output consensus algorithm extended from DFD for a class of leader-follower MAS is provided, which not only completely suppresses disturbance, but also avoids chattering. Finally, several simulation examples are given to verify the effectiveness of the DFD.
Paper Structure (15 sections, 38 equations, 5 figures)

This paper contains 15 sections, 38 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Necessary preparation
  3. Graph theory
  4. Some useful lemmas
  5. Motivations
  6. Distributed finite-time differentiator
  7. Problem statement
  8. Design of a distributed finite-time differentiator via relative position information
  9. Design of distributed finite-time differentiator via absolute position information
  10. Design of distributed finite-time consensus controller for leader-follower MAS
  11. Numerical examples and simulations
  12. Distributed finite-time differentiator via relative position information
  13. Distributed finite-time differentiator via absolute position information
  14. Distributed finite-time consensus controller
  15. Conclusion

Figures (5)

  • Figure 1: Communication topology A among agents.
  • Figure 2: The response curves of relative position estimation under communication topology A.
  • Figure 3: The response curves of relative velocity estimation under communication topology A.
  • Figure 4: The response curves of absolute position estimation and absolute velocity estimation under communication topology A.
  • Figure 5: The response curves of MAS' output and control input under communication topology A.