Consensus control of multi‐agent systems with switched linear dynamics

• Published in: IET control theory & applications 2023-12, Vol.17 (18), p.2474-2484
• Main Author: Zhu, Yan
• Format: Article
• Language: English
• Subjects: Communication; Control methods; control system analysis; Control systems; Control theory; Controllability; controllers; Dynamics; Eigenvalues; Graph theory; Linear systems; multi‐agent systems; System effectiveness; Topology
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/cth2.12532

In this work, the consensus problem of multi‐agent systems is addressed whose agent dynamics are described by the switched linear system, and the interaction topology is a directed graph. Two cases are considered: For completely controllable agent dynamics, a novel construct method of control law and switching signal are proposed to derive sufficient conditions to solve the finite‐time consensus problem. When the controllability of the agent system is incomplete, it is proven that the uncontrollable sub‐mode of agent dynamics is consistently asymptotically stabilizable is a key condition to achieve consistency for multi‐agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results obtained in this paper. We proposed a new method to design control input and switching signals. And proved that, multi‐agent systems can achieve consensus if the uncontrollable sub‐mode is consistently stabilizable and all nonzero eigenvalues of the Laplace matrix of the communication topology are equal. And a completely controllable multi‐agent system can achieve finite‐time consensus, and the time is less than n(n+1)/2τ(N−1)$n(n+1)/2 \tau (N-1)$.