Abstract
Consensus of fractional-order multiagent systems (FOMASs) with single integral has been wildly studied. However, the dynamics with multiple integral (especially double integral to sextuple integral) also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems (MIFOMASs) with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results.
Highlights
The research related to multiagent systems (MASs) has been going on for decades, due to its many meaningful applications, e.g., sweep coverage control of MASs [1], flocking behavior of mobile robots [2], and coordinated attitude control of a formation of satellites [3]
Suppose that a fractional-order multiagent systems (FOMASs) with multiple integral is given by MIFOMAS ( ) whose corresponding network topology G satisfies Lemma
If we suppose that a FOMAS with multiple integral is given by MIFOMAS ( ) whose corresponding network topology G satisfies Lemma and α1 = α2 = ⋅ ⋅ ⋅ = αl = 1, the MIFOMAS ( ) with symmetric time-delays can be transformed into high-order MAS with symmetric time-delays whose dynamic model is an integer-order dynamic model and the following functions can be obtained: l
Summary
The research related to multiagent systems (MASs) has been going on for decades, due to its many meaningful applications, e.g., sweep coverage control of MASs [1], flocking behavior of mobile robots [2], and coordinated attitude control of a formation of satellites [3]. Authors in [27, 28] indicated that the integer-order systems were only the special examples of the fractionalorder systems Based on these facts, the research results on consensus of FOMASs with single integral in [29,30,31,32,33,34] have been continuously springing up in recent years. The above research results on the consensus problems of FOMASs with or without time-delays were based on the single-integral fractionalorder or double-integral fractional-order dynamics. To this day, there is almost no research on consensus problems of MIFOMASs with time-delays, especially nonuniform timedelays.
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