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In this article, a novel dynamic periodic event-triggered control (DPE-TC) is proposed to investigate input-to-state stability (ISS) in multilayer coupled systems (MCSs). Different from the existing literature, a dynamic term is introduced to event-triggered control (E-TC), which can reduce the number of event triggers as the interexecution times are prolonged on the whole. Moreover, a periodic sampling is adopted, from where the Zeno phenomenon is naturally avoided. Based on the Lyapunov method and graph theory, ISS for coupled systems under the DPE-TC is established. Meanwhile, a dynamic event-triggered control with dwell-time is proposed, and a corollary to ensure the ISS of MCSs is also provided. Eventually, results are applied to second-order oscillators and a numerical example is given to prove the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization problem for multi-weighted complex networks via alternate event-triggered aperiodically intermittent control (AETAIC) is considered. Different from existing literature, the proposed AETAIC is triggered alternatively by two pre-defined conditions. In contrast to the conventional event-triggered control, the event-triggered conditions of AETAIC can not only judge the updates of control signals, but also dominate the actuation and close of the control. Through graph theory and Lyapunov method, several sufficient conditions are given to ensure exponential synchronization of the studied networks. Moreover, a positive lower bound of the inter-execution is obtained, such that Zeno behavior can be excluded. Finally, in order to illustrate the theoretical results, two practical applications about Chua's circuits and coupled oscillators are presented. Meanwhile, numerical simulations are provided to validate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

In this paper, an alternate event-triggered control is proposed to achieve stability of interval type-2 Takagi–Sugeno fuzzy systems. Comparing with the existing literature, this new control strategy displays an almost complete aperiodic feature which eliminates the conservativeness caused by time-triggered property of the traditional aperiodically intermittent control. Moreover, with two events being triggered alternately in this control strategy through examining two predetermined conditions, the efficiency of control can be further improved and the resources consumption can be greatly reduced. By employing the Lyapunov function and graph theory, several stability criteria are rigorously demonstrated. In addition, Zeno behavior is excluded in our system through obtaining a positive lower bound of the time interval between two triggering points. Subsequently, the validity of the presented strategy is evidenced by single-link robot arms systems. Finally, a numerical example is given to lend insight into the feasibility of our theoretical results. • A kind of alternate event-triggered aperiodically intermittent control is proposed. Under the two prescribed event-triggered conditions, the alternate triggering of two events and the intermittent control input can be achieved. • Compared with previous results, the proposed control strategy combines the advantages of event-triggered control and intermittent control. • The stability criteria are given through utilizing the Lyapunov function and graph theory. [ABSTRACT FROM AUTHOR]

In this paper, bipartite synchronization of signed networks with stochastic disturbances via aperiodically intermittent control is investigated. The aperiodically intermittent control presented is based on discrete-time state observations rather than continuous-time ones. To formulate signed networks and exhibit the competitive relation, a structurally balanced signed network is built and all the units are divided into two subcommunities. By employing Lyapunov method and graph theory, some sufficient conditions on bipartite synchronization are given. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control and feedback control respectively, two corollaries are also provided to ensure the bipartite synchronization of the signed networks. Ultimately, two applications to coupled single-link robot arms and coupled oscillators are presented and corresponding numerical examples are respectively provided to verify the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates finite-time synchronization for fuzzy cellular neural networks (FCNNs). In contrast to correlative studies, discrete time delays, distributed delays and stochastic perturbations are taken into consideration. A mathematical model of this kind of FCNN is considered for the first time. By employing the Lyapunov method, graph theory, the feedback control technique and stochastic finite-time synchronization theory, several sufficient conditions for finite-time synchronization of FCNNs are derived. The upper bound of the stochastic settling time is explicitly proposed and has a close relationship with the topological structure of the neural network. Finally, a numerical example is used to validate the practicability and feasibility of the theoretical results we propose. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time synchronization problem for multi-coupling fuzzy cellular neural networks (FCNNs) with stochastic perturbations and mixed delays is addressed. Compared with exponential synchronization and asymptotic synchronization in existing literature, finite-time synchronization of stochastic FCNNs is studied for the first time, which is of better significance. Combining graph-theoretical technique and Lyapunov method, under the framework of feedback control, some finite-time synchronization conditions are derived. Besides, from the perspective of the connectedness of FCNNs, we just demand at least one directed path on the digraph between different vertices in networks, instead of each sub-network. Then, the convergence time is explicitly proposed, which is connected with the parameters of control and topological structure of networks. Eventually, a numerical example is also carried out to demonstrate the practicability and validity of our proposed results. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates finite-time synchronization for fuzzy Cohen–Grossberg neural networks (FCGNNs) with mixed delays and discontinuous activations via state-feedback control. The features of FCGNNs, discrete time delays, distributed delays and discontinuous activations are taken into account which makes our networks more general and practical in comparison with the most existing Cohen–Grossberg neural networks. Two switching state-feedback controllers designed for the implement of finite-time synchronization can be used to effectively overcome the limitations of the traditional continuous linear feedback controllers. Different from previous work, graph theory and Lyapunov method are used to study finite-time synchronization of FCGNNs for the first time in this paper, then some sufficient criteria are obtained to guarantee the finite-time synchronization of FCGNNs. In particular, it is worth noting that the settling time for finite-time synchronization is closely related to the topological structure of FCNNs. Finally, two numerical examples are given to verify the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies a min–max location-routing problem, which aims to determine both the home depots and the tours for a set of vehicles to service all the customers in a given weighted graph, so that the maximum working time of the vehicles is minimized. The min–max objective is motivated by the needs of balancing or fairness in vehicle routing applications. We have proved that unless , it is impossible for the problem to have an approximation algorithm that achieves an approximation ratio of less than 4/3. Thus, we have developed the first constant ratio approximation algorithm for the problem. Moreover, we have developed new approximation algorithms for several variants, which improve the existing best approximation ratios in the previous literature. [Copyright &y& Elsevier]