Finite Time Adaptive Sliding Mode Control of Multi-agent Systems via Unknown External Disturbance and Undirected Network

Document Type : Dynamics, Vibrations, and Control

Author

Assistant Professor, Department of Mechanical Engineering, Faculty of Engineering, Ayatollah Boroujerdi University, Boroujerd, Iran

Abstract

In this paper, the finite time control of 2nd order multi-agent systems (MASs) consisting of a leader and a number of followers under external disturbance is discussed. The communication graph of agents is considered non-directional and the distance between them is considered constant. The goal is to design a robust adaptive sliding mode controller which, by estimating the upper and lower limits of the disturbance, not only ensures the finite time stability of the system, but also does not increase the tracking error range between the agents. For this purpose, a new slip surface is defined, which becomes zero under the considered controller, both of the above goals are met. The second Lyapunov theorem is used to prove the stability of the system and an unbounded radial Lyapunov function is presented in terms of the new slip surface and estimation errors. Based on the communication structure of the factors, the necessary control and adaptive rules will be obtained to make the derivative of the Lyapunov function negative. The results are presented in the form of a theorem with proof. In order to validate this method, two scenarios with different movements of the leader are examined. It is shown that the mentioned system is finite time stable under the presented control method and the tracking error between the agents reaches zero.

Highlights

  • The proposed adaptive sliding mode control assures the finite time stability of the multi-agent system
  • The external disturbance is assumed bounded and unknown
  • Under the proposed control, the amplitude of distance error between agents will decrease

Keywords

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References

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Aerospace Mechanics
Volume 19, Issue 3 - Serial Number 73
Serial No. 73, Autumn Quarterly
December 2023
Pages 137-148

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History

  • Receive Date: 01 February 2023
  • Revise Date: 17 April 2023
  • Accept Date: 07 May 2023
  • Publish Date: 21 April 2023

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