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.
Highlights
In recent years, since multi-agent systems (MASs) accomplish their functions via communication and coordination among various agents, they exhibit much higher work efficiency and performance than single system
Many scholars have studied the cooperative control of fractional-order multi-agent systems (FOMASs) [7]–[9]
The problem formulation and main results regarding input delayed fractional-order multi-agent systems with P and PDα fractional-order iterative learning control are discussed in Sections 3 and 4, respectively
Summary
Since multi-agent systems (MASs) accomplish their functions via communication and coordination among various agents, they exhibit much higher work efficiency and performance than single system. FOMASs. Zhu et al [20] designed a control gain matrix based on graph theory and the Riccati equations to achieve sufficient conditions for linear FOMASs. in the literature [21], the consensus problem of linear and nonlinear fractional multi-agent systems with time delay is studied. Deng et al [31] proposed a high-order ILC for solving the tracking control problem of nonlinear multi-agent systems with time-varying delays and a directed topology. Considering the leader-following consensus problem for the systems, two distributed fractional-order iterative learning control (FOILC) methods, open-loop PDαtype and open-loop Dα-type FOILC are proposed to realize consensus convergence of the system within a limited time. The problem formulation and main results regarding input delayed fractional-order multi-agent systems with P and PDα fractional-order iterative learning control are discussed in Sections 3 and 4, respectively.
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