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

Abstract

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. INDEX TERMS Fractional-order system, multi-agent system, iterative learning control, consensus tracking, communication time delays.

Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy

“…Remark 1. Unlike in the literature [40][41][42] in the original text on system modeling, which investigates integer-order time delay for discrete systems, this paper considers fractional-order distributed time delay. The propagation delays are distributed over a period of time and may influence the control system to oscillate more.…”