Abstract
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 α -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 α -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 α -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 α type learning scheme in this paper.
Highlights
During the past decade, consensus analysis and cooperative control of multi-agent systems (MASs) have attracted extensive attention from scholars of different fields on account of their potential applications in several areas such as cooperative transportation by mobile robots [1], flocking [2], and formation control of vehicles [3], and so on
In [16], [17], the formation control problems of nonlinear MASs under switching interaction topologies were addressed by employing the Iterative learning control (ILC) scheme
In view of the above discussion, the main purpose of this paper is that the closed-loop Dα-type iterative learning update controllers with initial state learning laws are constructed for linear and nonlinear SFOMASs to achieve perfectly consensus tracking performances of the follower agents under iteration-varying switching topologies and initial state errors over a finite time interval
Summary
Consensus analysis and cooperative control of multi-agent systems (MASs) have attracted extensive attention from scholars of different fields on account of their potential applications in several areas such as cooperative transportation by mobile robots [1], flocking [2], and formation control of vehicles [3], and so on. Iterative learning control (ILC) has been widely utilized to cope with the repeated tracking control with high precision requirement in the fixed time interval due to its simplicity and effectiveness [8], [9]. ILC has been successfully implemented to many kinds of multi-agent systems in recent references, such as high-order nonlinear MASs [10], singular MASs [11], fractional-order MASs [12], and distributed parameter MASs [13]–[15], etc. To handle the consensus tracking without a priori knowledge of the control direction, a new adaptive iterative learning control protocol was developed for uncertain nonlinear multi-agent systems under the fixed topology in [18]. The authors have investigated the problem of quantized iterative learning [19]–[21], and some practical factors including the finite-leveled quantizer with random
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