Fixed-Time Cluster Synchronization of Discontinuous Directed Community Networks via Periodically or Aperiodically Switching Control

Abstract

The fixed-time cluster synchronization problem for a class of directed community networks with linear couplings and discontinuous nodes is investigated in this paper. First, by means of reduction to absurdity and mathematical induction, two new and vital differential equalities are proposed and proved to study the fixed-time stability. Besides, by designing periodically switching controllers and aperiodically adaptive switching controllers, as well as using the theory of differential inclusions, some fixed-time cluster synchronization criteria are derived in which the settling time function is bounded for any initial values. Finally, the numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem. INDEX TERMS Fixed-time synchronization, cluster synchronization, directed community networks, switching control, differential inclusions.

Fixed‐time synchronization of stochastic complex networks with Markov jump and mixed delays via adaptive non‐chattering control

“…The fuzzy neural networks mentioned in References 25,34 is more practical, so we will consider the fixed‐time synchronization of fuzzy neural networks with stochastic perturbations in the future; 2. Due to the increasing importance of aperiodically intermittent control, 35,36 in future work, the fixed‐time synchronization of CNs via aperiodically intermittent control is also one of the topics we are interested in.…”

Fixed-time cluster consensus for multi-agent systems with objective optimization on directed networks

“…Assumption 2 states that the information exchange between agents in any two subgraphs should be balanced. This is accepted in existing publications [15][16][17][18][19][20][21]. In [15][16][17][18][19][20][21], competitive and cooperative relationships are introduced to emphasize the information communication difference between agents in the same subgroups and different subgroups.…”

“…Clearly, complete consensus is a special case of cluster consensus. Cluster consensus, as a branch of cluster synchronization [15,16] has obtained widely attention from researchers. For example, the cluster consensus of MASs with Markovian switching topologies and communication noise was discussed in [17].…”

Finite/fixed-time synchronization for complex networks via quantized adaptive control

“…In order to overcome the above-mentioned drawbacks of finite-time control, the concept of fixed-time convergence is proposed in [23]. Recently, according to this idea, the corresponding research results of fixed-time synchronization control have been presented in [30,31,8]. In [30], the continuous pinning controller has been designed for the complex networks, and the sufficient condition has been obtained to ensure the fixed time synchronization of complex networks.…”

“…Therefore, more researches have been focused on the fixed-time synchronization control for a class of complex networks with random noise disturbance, and the Itô integral principle has been proposed to solve the problem such as [31]. For a type of cluster networks with linear coupling and discontinuous nodes, the differential inclusion principle has been used to obtain the fixed-time cluster synchronization criterion in [8].…”