Finite-time cluster synchronization for time-varying delayed complex dynamical networks via hybrid control

Abstract

Throughout this article, the conundrum on finite-time cluster synchronization is investigated for time-varying delayed complex dynamical networks using a kind of new hybrid control scheme. In the light of Lyapunov stability theorem and finite-time control theory, the finite-time cluster synchronization criteria can be achieved. Besides, we introduce the distinction between cluster synchronization and complete synchronization, which is how to select the controlling nodes. We discuss the differences among cluster synchronization with time-varying delays, complete synchronization with time-varying delays, cluster synchronization with a single delay, and cluster synchronization without delay, which is on constructing Lyapunov functional and designing the finite-time hybrid controllers. Finally, numerical simulations are presented to demonstrate the availability of the theoretical consequences.

Finite-Time Synchronization and Identification between Two Nonlinear Coupled Multiweighted Markovian Switching Delayed Networks with Uncertain Models and External Disturbances

“…In the follow, according to the controller (20) and condition (21), some control parameters of controller (20) are selected as η(1) � η(2) � 10; k (1) � 12, k (2) � 15; λ(1) � λ(2) � 15; μ(1) � 24, μ(2) � 18; φ(1) � φ(2) � 5; ψ(1) � 9, ψ(2) � 4; ϕ(1) � ϕ(2) � 15; c � 0.6; M α � 100, M β � 100, M α � 100, and M v � 100. In this simulation process, the start time of the simulation is selected at t 0 � 0 and time delay τ � 0.01.…”

“…Mathematical Problems in Engineering delayed networks ( 10) and ( 14) can be achieved under the controller (20) and inequality condition (21). According to Lemma 1, the finite-time t 1 can be expressed as follows:…”

“…Remark 4. In the synchronization and parameters identification process between two Markovian switching networks, the speed of synchronization and unknown parameters identification will be affected by these control parameters η i , k, λ i , μ i , φ, ϕ i , ψ i , Δ i , v i in controller (20).…”

“…In actual engineering, people not only pay attention to its gradual stability characteristics in infinite time but also are more interested in realizing the synchronization state of the system in a finite time, such as aerospace systems, robot control systems, and power systems; they are often required that the synchronization be reached in a finite time. e finite-time control technology can realize this idea, and the finite-time control scheme can make the network have better robustness [20]. In [15], the author investigated finite-time synchronization of complexed-valued neural networks with multiple time-varying delays and infinite distributed delays.…”

Finite‐Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

“…However, few studies explore the finite-time synchronization of uncertain complex networks. Xiao et al [28] studied the finite-time cluster synchronization of a complex dynamic network with time-varying delay by using the hybrid control strategy; literature [29] used the average dwell time method to obtain some sufficient conditions for realizing finite-time synchronization of sampled-data T-S fuzzy complex dynamic networks. But, both of them considered the case where the relationship between the nodes is linearly coupled, and they do not consider the uncertainties that may be contained in the system.…”