Cascade Super-Twisting Observer for Linear Multi-Agent Systems Without Communication

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The paper addresses the consensus problem (i.e., the agreement of phase vectors) for a multi-agent system consisting of identical linear agents. The study focuses on the case where there is no communication between agents, meaning there is no exchange of information, and agent control is achieved through the agents’ own sensors, providing incomplete information about the phase vector of the agent and its neighbors, with the information possibly being noisy. To solve this problem, a linear protocol based on observer data for systems under uncertainty is proposed. Cascade observers based on the “super-twisting” method are suggested as such observers. Sufficient conditions for the existence of a controller are obtained, where the observation error converges to zero under limited disturbances. An example illustrating the proposed approach is provided. 

Full Text

Restricted Access

About the authors

V. V. Fomichev

Hangzhou Dianzi University; Federal Research Center “Informatics and Control” of RAS; Lomonosov Moscow State University

Author for correspondence.
Email: fomichev@cs.msu.su
China, Hangzhou; Moscow, Russia; Moscow, Russia

A. I. Samarin

Lomonosov Moscow State University

Email: samarin_aleksei@icloud.com
Russian Federation, Moscow

References

  1. Dorri, A. Multi-agent systems: a survey / A. Dorri, S.S. Kanhere, R. Jurdak // IEEE Access. — 2018. — V. 6. — P. 28573–28593.
  2. Hamann, H. Swarm Robotics: A Formal Approach / H. Hamann. — Cham : Springer, 2018.
  3. Saber, R.O. Consensus protocols for networks of dynamic agents / R.O. Saber, R.M. Murray // Proceed. of the 2003 American Control Conf. — Denver, Colorado, USA : IEEE, 2003. — V. 2. — P. 951–956.
  4. Li, Z. Dynamic consensus of linear multi-agent systems / Z. Li, Z. Duan, G. Chen // IET Control Theory
  5. Appl. — 2011. — V. 5, № 1. — Art. 19.
  6. Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies / W. He, D. Xu, Q.-L. Han, F. Qian // IEEE Trans. Cybern. — 2020. — V. 50, № 7. — P. 2996–3008.
  7. Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint / Z. Li, Z. Duan, G. Chen, L. Huang // IEEE Trans. Circuits Syst. I. — 2010. — V. 57, № 1. — P. 213–224.
  8. A new observer-type consensus protocol for linear multi-agent dynamical systems / Y. Zhao, G. Wen, Z. Duan
  9. [et al.] // Asian J. Control. — 2013. — V. 15, № 2. — P. 571–582.
  10. Fomichev, V.V. Algorithm for designing a cascade asymptotic observer for a system of maximal relative order / V.V. Fomichev, A.O. Vysotskii // Differ. Equat. — 2019. — V. 55, № 4. — P. 553–560.
  11. Sliding mode fault tolerant consensus control for multi-agent systems based on super-twisting observer / P. Yang, X. Hu, Z. Wang, Z. Zhang // J. of Syst. Engineer. and Electron. — 2022. — V. 33, № 6. — P. 1309–1319.
  12. Emelyanov, S.V. A new class of second-order sliding mode algorithms / S.V. Emelyanov, S.K. Korovin, L.V. Levantovsky // Matematicheskoye modelirovaniye. — 1990. — V. 2, № 3. — P. 89–100. [in Russian]
  13. Seeber, R. Necessary and sufficient stability criterion for the super-twisting algorithm / R. Seeber, M. Horn // 15th Intern. Workshop on Variable Structure Systems (VSS). Graz : IEEE, 2018. — P. 120–125.
  14. Bagge Carlson, F. ControlSystems.jl: a control toolbox in Julia / F. Bagge Carlson, M. F¨alt, A. Heimerson, O. Troeng // 60th IEEE Conference on Decision and Control (CDC). Austin, TX, USA: IEEE, 2021. — P. 4847–4853.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Communication graph.

Download (21KB)
Indexing metadata
3. Fig. 2. Protocol comparison (lines connect the points corresponding to the Pareto-optimal pairs . It can be seen that for every pair of protocol without communication (1), there is a pair of protocol with communication (2) that better suppresses both interferences.

Download (37KB)
Indexing metadata
4. Fig. 3. Comparison of consensus error when applying the linear protocol (1) and the new approach (2) a, and an example of an external perturbation for a single agent b.

Download (101KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences