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Summary: In this article, the cluster consensus problems of two classes of nonlinear multi‐agent systems (NMASs) are studied under the dynamic event‐triggered control (ETC) strategy, where cooperative‐competitive interactions among agents and high‐order dynamics are considered. First, two dynamic ETC protocols are developed to realize the cluster synchronization of NMASs. Different from the static ETC, a dynamic parameter regulated by an adaptive law is used in place of a constant which can improve the trigger time intervals and reduce the energy consumption. Subsequently, an adaptive control mechanism based on the proposed ETC strategy is designed to adjust the controller parameter for agents. Some sufficient conditions for achieving the cluster consensus of NMASs are derived by using the Lyapunov stability theory and algebraic graph theory. Moreover, it is proved in theory that Zeno phenomenon can be excluded with these control schemes. Finally, two simulation examples validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the cluster consensus problems of two classes of leader-following nonlinear multi-agent systems (LFNMASs). The event-triggered strategies are applied to solve the problems, which can significantly reduce energy consumption and the frequency of the controller updates. The sufficient conditions are presented to realize the cluster consensus for two classes of LFNMASs. Then, it is proved that the Zeno behavior can be avoided under the proposed event-triggered control strategies. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Acridone‐functionalized carbazole dendrimers were synthesized via copper‐catalyzed Ullmann amination and their properties were investigated by spectroscopic and electrochemical measurements, as well as theoretical calculations. The results reveal that the properties of the carbazole dendrimers vary according to the position of acridone. Intramolecular charge transfer between the acridone core and the outer carbazole dendron is observed, accompanying a red shift of the emission maximum and a decline of quantum yields with the rise of the dendrimer generation. Whereas the internal carbazole unit has little influences on the photoluminescence of dendrimers with acridone at the periphery in solution. The electrochemical analysis and theoretical calculations demonstrate a convergence in HOMO and LUMO energy levels in dendrimers bearing the acridone core and a decrease in both of these energy levels in dendrimers with the acridone at the periphery when the dendrimer generation increases. [ABSTRACT FROM AUTHOR]

A variety of N‐substituted acridone derivatives were synthesized to make a comparison of their properties according to the number of acridone unit and the nature of substituent. The spectroscopic and electrochemical investigations show that the properties of N‐substituted acridone derivatives are substituent‐dependent. With benzene, biphenyl, fluorene and carbazole as linkers, the acridone derivatives demonstrate the properties of acridone itself due to a very weak intramolecular charge transfer (ICT) between acridone and the linker. However, significant ICT process is observed when the electron withdrawing groups are involved to form the donor–acceptor systems with acridone as the electron donating groups, which is different from the previously reported results of which acridone is usually used as an electron acceptor. Moreover, thermally activated delayed fluorescence (TADF) is observed with anthraquinone as linker. The theoretical calculations reveal that the N‐substitutions have more influences on the locations and energy levels of the LUMOs than those of the HOMOs. [ABSTRACT FROM AUTHOR]

Length‐defined 2,7‐acridone oligomers were synthesized via a sequence of bromination, borylation and Suzuki–Miyaura cross‐coupling reaction. Both the single crystal structure analysis and the theoretical calculations demonstrate that the anti conformation is favored in the oligomer. The relationship of the properties and the number of acridone units in the oligomer was investigated. The UV/Vis absorption and fluorescence spectroscopy reveal that the absorption and emission of oligomers are red‐shifted and energy gaps narrow with the increase of acridone moieties, as well as a decline in the radiative decay rate. Cyclic voltammetry measurements and theoretical calculations elucidate that the quantity of acridone in the oligomer plays a greater effect on the HOMO energy levels than on the LUMO ones. [ABSTRACT FROM AUTHOR]