| Summary: | This paper investigates the leader-following consensus tracking problems via iterative learning control for singular fraction-order multi-agent systems in the presence of iteration-varying switching topologies and initial state errors. First, in order to eliminate the impulsive effect of singular systems and handle iteration-varying topologies, the closed-loop D<sup>α</sup>-type iterative learning control protocol is proposed. To deal with initial state errors, the initial state learning laws are introduced in light of the initial output errors of each follower agent. The developed D<sup>α</sup>-type learning protocols based on initial state learning laws can guarantee each follower track perfectly the leader agent in the fixed time interval. Next, the sufficient convergent conditions of consensus tracking errors are provided. Moreover, the D<sup>α</sup>-type learning protocols are extended to nonlinear singular fraction-order multi-agent systems with iteration-varying topologies and initial state errors. Finally, two numerical examples are presented to verify the validity of the proposed D<sup>α</sup> type learning scheme in this paper.
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