Decentralized leader-following consensus control design for discrete-time multi-agent systems with switching topology

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2024.2.08

Keywords:

multi-agent system, consensus control, switching topology, PID controller, invariant ellipsoids method, linear matrix inequality, semidefinite programming problem

Abstract

The problem of consensus control of linear discrete-time multi-agent systems (MASs) with switching topology is considered in the presence of a leader. The goal of consensus control is to bring the states of all agents to the leader state while providing stability for local agents, as well as the MAS as a whole. In contrast to the traditional approach, which uses the concept of an extended dynamic multi-agent system model and communication topology graph Laplacian, this paper proposes a decomposition approach, which provides a separate design of local controllers. The control law is chosen in the form of distributed feedback with discrete PID controllers. The problem of local controllers’ design is reduced to a set of semidefinite programming problems using the method of invariant ellipsoids. Sufficient conditions for agents’ stabilization and global consensus condition fulfillment are obtained using the linear matrix inequality technique. The availability of information about a finite set of possible configurations between agents allows us to design local controllers offline at the design stage. A numerical example demonstrates the effectiveness of the proposed approach.

Author Biographies

Yurii Dorofieiev, National Technical University “Kharkiv Polytechnic Institute”, Kharkiv

Professor, Doctor of Technical Sciences, the head of the System Analysis and Information-Analytical Technologies Department of National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine.

Leonid Lyubchyk, National Technical University “Kharkiv Polytechnic Institute”, Kharkiv

Doctor of Technical Sciences, a professor at the Department of Computer Mathematics and Data Analysis of National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine.

Maxim Malko, National Technical University “Kharkiv Polytechnic Institute”, Kharkiv

Associate professor, Candidate of Technical Sciences (Ph.D.), a professor at the System Analysis and Information-Analytical Technologies Department of National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine.

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Published

2024-06-28

Issue

No. 2 (2024)

Section

Mathematical methods, models, problems and technologies for complex systems research

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