Modified function projective synchronization of complex dynamical networks with mixed time-varying and asymmetric coupling delays via new hybrid pinning adaptive control

Abstract

This paper investigates modified function projective synchronization (MFPS) for complex dynamical networks with mixed time-varying and hybrid asymmetric coupling delays, which is composed of state coupling, time-varying delay coupling and distributed time-varying delay coupling. In contrast to previous results, the coupling configuration matrix needs not be symmetric or irreducible. The MFPS of delayed complex dynamical networks is considered via either hybrid control or hybrid pinning control with nonlinear and adaptive linear feedback control, which contains error linear term, time-varying delay error linear term and distributed time-varying delay error linear term. Based on Lyapunov stability theory, adaptive control technique, the parameter update law and the technique of dealing with some integral terms, we will show that control may be used to manipulate the scaling functions matrix such that the drive system and response networks could be synchronized up to the desired scaling function matrix. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works.

Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

“…[34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization. [34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization.…”

“…In general, complex networks are difficult to synchronize by themselves, and many control technologies such as sliding-mode control, impulsive control, intermittent control, and some hybrid control methods were introduced to actuate networks to the objective states. [34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization. In the work of Ma and Wang, 38 by using periodically pinning intermittent control, some synchronization criteria were derived for delayed networks; in the work of Liang and Wang, 39 the authors studied the synchronization problems in virtue of intermittent control with two switched periods; in a further step, intermittent control with multiple switched periods was also extended.…”

Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays

“…Many important synchronization control methods have also been developed for CDNs, for instance, feedback control [10,11], intermittent control [4,5], sampled-data control [30], nonlinear feedback control [9,32], pinning control [14,29,33,43], adaptive control [25,31,40,45], pinning adaptive control [19,25,31,39], and other control methods. When controlling a real plant, it is always desirable to design a control system not only asymptotical stability but also guaranteed adequate level of performance.…”

Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings

“…Figure 14 shows the FPS errors between the states of isolate node ( ) ( ) of (45) and node ( ) of (47), where ( ) = ( ) − ( ) ( ) for = 1, 2, = 1, 2, 3, without nonlinear and adaptive control (34). Figure 15 shows the FPS errors between the states of isolate node ( ) ( ) of (45) and node ( ) of (47), where ( ) = ( ) − ( ) ( ) for = 1, 2, = 1, 2, 3, with nonlinear and adaptive control (34). Figure 16 gives the evolution of adaptive feedback gains 11 ( ), 21 ( ), and 31 ( ).…”

“…Meanwhile, various selection rules of pinned nodes have been introduced in the existing literatures. The pinned nodes selection rules according to the out-degree and in-degree of the nodes and the synchronization problem were studied for undirected and directed networks which was presented in [25,26,34]. The pinning control problem of neural networks was considered and then some unexceptional pinning conditions were found out [27][28][29], while Chen et al [35] expressed that, even applying one single pinned node, the whole networks could be controlled as long as the coupling strength was large enough.…”