Consensus Control of Fractional-Order Multi-Agent Systems With Time Delays via Fractional-Order Iterative Learning Control

• Published in: IEEE access Vol. 7; pp. 159731 - 159742
• Main Authors: Lv, Shuaishuai, Pan, Mian, Li, Xungen, Cai, Wenyu, Lan, Tianyi, Li, Bingqiang
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; communication time delays; consensus tracking; Convergence; Delay effects; Fractional calculus; Fractional-order system; Graph theory; Iterative learning control; Machine learning; multi-agent system; Multi-agent systems; Multiagent systems; Stability analysis; Tracking problem
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2950302

This paper considers the leader-following consensus tracking problem of fractional-order multi-agent systems (FOMASs) that contain communication time delays. By combining the iterative learning control (ILC) approach and fractional-order calculus, a distributed PD α -type fractional-order iterative learning control (FOILC) and a distributed D α -type FOILC algorithm are proposed, respectively. Based on graph theory and λ-norm theory, the consensus problems of the proposed algorithms are discussed, and their convergence conditions are identified. The theoretical analysis demonstrates that as the number of iterations increases, all fractional-order agents with communication time delays can realize consensus exactly on the desired output trajectory by selecting suitable gain matrices of FOILC over a finite time interval. Illustrative examples are presented, on which the performances of the proposed method are evaluated.