Abstract
Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.
Highlights
Consensus problems of multiagent systems have attracted a great deal of attention due to their enormous potential applications in many areas such as the formation control of multirobot systems [1], cooperative control of unmanned aerial vehicles [2], and distributed information filtering [3]
Motivated by the previous analysis, this paper investigates consensus problems for the two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: the FOMAS with symmetric time delays and undirected topology and the FOMAS with asymmetric time delays and directed topology
2, 3, and 4, we can find that when all the time delays stay away from the delay margin τ when the communication topology and the fractional order α of the FOMAS stay the same, the convergence speed will become faster, whereas the convergence speed will become slower when all the time delays get close to the delay margin τ
Summary
Consensus problems of multiagent systems have attracted a great deal of attention due to their enormous potential applications in many areas such as the formation control of multirobot systems [1], cooperative control of unmanned aerial vehicles [2], and distributed information filtering [3]. As is known to us, the essential characteristic or behavior of an object in the complex environment can be better revealed using the fractional-order dynamical model [13]. The fractional-order and compound-order multiagent cooperative control protocols with communication delays were studied in [24, 25], and the time delays contained up to n different values when FOMAS was composed of n agents. The main innovation of this article lies in the research on the fractional-order dynamics which can better reveal the essential characteristic or behavior of an object in the complex environment and the consensus of FOMAS with asymmetric time delays which contain up to n(n−1) different values when FOMAS consists of n agents. The fractional consensus algorithms for multiagent dynamical systems with different types of time delays are studied in Sections 3 and 4.
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