Exponential Finite-Time Consensus of Fractional-Order Multiagent Systems

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 4; pp. 1549 - 1558
• Main Authors: Liu, Huiyang, Cheng, Long, Tan, Min, Hou, Zeng-Guang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Convergence; Directed network topology; exponential finite-time consensus; fast sliding-mode algorithms; fractional-order dynamics; Graph theory; Heuristic algorithms; Liapunov functions; Lyapunov methods; Manifolds; Multi-agent systems; Multiagent systems; Protocols; Sliding mode control
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2018.2816060

The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-mode manifold (surface) vector is defined, and then the fractional-order multiagent system is transformed into an integer-order (namely, first-order) multiagent system. Second, based on the fast sliding-mode control technique, a protocol is proposed for the obtained first-order multiagent system. Third, a new Lyapunov function is presented. By suitably estimating the derivative of the Lyapunov function, the reachability of the sliding-mode manifold is derived. It is proved that the exponential finite-time consensus can be achieved if the communication network has a directed spanning tree. Finally, the effectiveness of the proposed algorithms is demonstrated by some examples.